MCQ 11 Mark
Choose the correct option: There is no perfect cube which ends in $4.$
AnswerWe know,
cube of $4$, i.e. $4^3 = 64,$ which is a perfect cube.
That is, there exists a perfect cube which ends in $4.$
Therefore, the given statement is false and option $B$ is correct.
View full question & answer→MCQ 21 Mark
The volume of a cubical box is $64cm^3.$ Which of the following is its side?
AnswerNow the Volume of a cube is given by $a^3.$
$64 = a^3$
$a = 4$
Hence the side is $4cm.$
View full question & answer→MCQ 31 Mark
Tick $(\checkmark)$ the correct answer: By what least number should $648$ be multiplied to get a perfect cube?
AnswerFactorising $648$,
We get,
$\begin{array}{c|c}2&648\\\hline2&324\\\hline2&162\\\hline3&81\\\hline3&27\\\hline3&9\\\hline3&3\\\hline&1\end{array}$
$648=2\times2\times2\times3\times3\times3\times3$
$=2^3\times3^3\times3$
$\therefore$ In order to get a perfect cube, we have to multiply by $3 \times 3$ to complete the triplet.
Required number $= 9$
View full question & answer→MCQ 41 Mark
Find the smallest number by which the number $625$ must be divided to obtain a perfect cube.
Answer$625 = 5 \times 5 \times 5 \times 5 = 5^3 \times 5.$
View full question & answer→MCQ 51 Mark
If the digit in one’s place of a number is $3,$ then the last digit of its cube will be:
AnswerIf the digit in one's place of a number is a, then the last digit of its cube will be the last digit of its cube.
Thus, if the digit in one's place of a number is $3,$ then the last digit of its cube will be unit digit of.
We know, the cube of $3,$ i.e. $3^3 = 27,$
Since the last digit of cube of $3$ is $7$
View full question & answer→MCQ 61 Mark
Find the smallest number by which the number $100$ must be multiplied to obtain a perfect cube.
Answer$100 = 2 \times 2 \times 5 \times 5.$
View full question & answer→MCQ 71 Mark
The one’s digit of the cube of the number $242$ is:
AnswerThe unit digit of $242$ is $2$
Cube of $2 = 2 \times 2 \times 2 = 8$
View full question & answer→MCQ 81 Mark
A perfect cube of a number having $0$ at its unit place, ends with _____ zeros.
Answer$10^3 = 1000$
$20^3 = 8000$
$30^3 = 27000$
View full question & answer→MCQ 91 Mark
If $(2744)^{1 / 3}=22 p+2 $ , then the value of $P$ is:
View full question & answer→MCQ 101 Mark
The smallest natural number by which $135$ must be divided to obtain a perfect cube is:
View full question & answer→MCQ 111 Mark
The cube of $−3.1$ is:
- ✓
$-29.791$
- B
$-2.6891$
- C
$-2.5781$
- D
AnswerCorrect option: A. $-29.791$
Cube of the number $−3.1:$
$(−3.1)3 = -3.1 × -3.1 × -3.1 = -29.791.$
Hence, option $A$ is correct.
View full question & answer→MCQ 121 Mark
The cube of an even natural number is:
Answer$6 \times 6 \times 6 = 216$ (even).
View full question & answer→MCQ 131 Mark
When the square of a number is subtracted from the cube of the same number, it becomes $100$. Find the number.
AnswerSquare of $5 = 5 \times 5 = 25$
Cube of $5 = 5 \times 5 \times 5 = 125$
$125 - 25 = 100$
View full question & answer→MCQ 141 Mark
The one’s digit of the cube of $53$ is:
Answer$53^3 = 53 \times 53 \times 53$
$3^3 = 3 \times 3 \times 3 = 27$
Hence, at the unit place, we will get $7$
Recheck: $53^3 = 53 \times 53 \times 53 = 148877$
View full question & answer→MCQ 151 Mark
Which of the following is false?
- A
Cube of any odd number is odd.
- B
A perfect cube does not end with two zeroes.
- C
The cube of a single digit number may be a single digit number.
- ✓
There is no perfect cube which ends with 8.
AnswerCorrect option: D. There is no perfect cube which ends with 8.
$1728 = 12^3$
View full question & answer→MCQ 161 Mark
The cube root of $13824$ is __________.
AnswerPrime factorisation of $13824$ is:
$13824 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3$
$13824 = (2 \times 2 \times 2) \times (2 \times 2 \times 2) \times (2 \times 2 \times 2) \times (3 \times 3 \times 3)$
Taking cube root both the sides, we get;
$(13824) = 2 \times 2 \times 2 \times 3 = 24$
View full question & answer→MCQ 171 Mark
Tick $(\checkmark)$ the correct answer: $(0.8)^3 = ?$
AnswerCorrect option: C. $0.512$
$(0.8)^3$
$= 0.8 \times 0.8 \times 0.8$
$= 0.512$
View full question & answer→MCQ 181 Mark
The cube of an even natural number is:
MCQ 191 Mark
Mark $(\checkmark)$ against the correct answer: Which of the following numbers is a perfect cube?
Answer$121 = 11 \times 11$
$169 = 13 \times 13$
$196 = 7 \times 7 \times 2 \times 2$
$216 = 2 \times 2 \times 2 \times 3 \times 3 \times 3$
$= (2)^3 \times (3)^3$
$= (6)^3$
$216 = (6)^3$
Hence, $216$ is a perfect cube.
View full question & answer→MCQ 201 Mark
What.is the value of $7^3 - 6^3?$
AnswerThe above of the two cube numbers can be found as
$7^3 - 6^3 = 6^2 + 7^2 + 6 \times 7$
$36 + 49 + 42 + = 127$
View full question & answer→MCQ 211 Mark
The square of a natural number subtracted from its cube is $48$. The number is:
View full question & answer→MCQ 221 Mark
Find the smallest number by which the number $10000$ must be divided to obtain a perfect cube:
Answer$10000 = 2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 5 \times 5$
$= 2^3 \times 2 \times 5^3 \times 5.$
View full question & answer→MCQ 231 Mark
Find the smallest number by which the number $2401$ must be divided to obtain a perfect cube.
Answer$2401 = 7 \times 7 \times 7 \times 7 = 7^3 \times 7.$
View full question & answer→MCQ 241 Mark
Cube of even natural number is _____ number.
AnswerWe know, the multiplication of $3$ even numbers, i.e. the cube of an even natural number, will always be even
Example, consider the even natural numbers $2$ and $4.$
Then, their cube is $2^3 = 8$ and $4^3 = 64,$ whose units place is even.
That is, the cubes are also even.
Hence, we can say, cube of even natural number is even.
Therefore, option $A$ is correct.
View full question & answer→MCQ 251 Mark
Which of the following numbers is a perfect cube?
Answer$125 = 5 \times 5 \times 5 = 5^3$
View full question & answer→MCQ 261 Mark
If $x$ is ones digit and $y$ is tens digit of a two digit number, then the cube of the number will be _________.
- ✓
$(10y + x)^3$
- B
$(10y + x)^2$
- C
$(10x + y)^3$
- D
AnswerCorrect option: A. $(10y + x)^3$
$(10y + x)^3$
View full question & answer→MCQ 271 Mark
If the digit in one’s place of a number is $6,$ then the last digit of its cube will be:
AnswerIf the digit in one's place of a number is a, then the last digit of its cube will be the last digit of its cube.
Thus, if the digit in one's place of a number is $6$, then the last digit of its cube will be unit digit of.
We know, the cube of $6$, i.e. $6^3 = 216,$
Since the last digit of cube of $6$ is $6.$
View full question & answer→MCQ 281 Mark
The one’s digit of the cube of the number $111$ is:
AnswerThe unit place of $111$ has $1$
Cube of $1 = 1^3 = 1 \times 1 \times 1 = 1$
View full question & answer→MCQ 291 Mark
Mark $(\checkmark)$ against the correct answer: $\sqrt[3]{216\times64}=\ ?$
Answer$\sqrt[3]{216\times64}$
$=\sqrt[3]{216}\times\sqrt[3]{64}$
$=\sqrt[3]{2\times2\times2\times3\times3\times3}\times\\\sqrt[3]{2\times2\times2\times2\times2\times2}$
$=\sqrt[3]{(2)^3\times(3)^3}\times\sqrt[3]{(2)^3\times(2)^3}$
$=\sqrt[3]{(6)^3}\times\sqrt[3]{(4)^3}$
$=6\times4$
$\sqrt[3]{216\times64}=24$
$\therefore\sqrt[3]{216\times64}=24$
View full question & answer→MCQ 301 Mark
The one’s digit of the cube of the number $111$ is:
Answer$1 \times 1 \times 1 = 1.$
View full question & answer→MCQ 311 Mark
Which among. the following the smallest number by which $7546$ is to be divided to make it a perfect cube?
AnswerThe prime factorization of $7546$ is:
$2 \times 7 \times 7 \times 7 \times 11$
Here, the primes $2$ and $11$ do not appear in group, of three.
So, we need to divide.
$7546$ by $2 \times 11 = 22$ to make it a perfect cube.
$\Rightarrow \frac{7546}{22}=343=(7)^3$
View full question & answer→MCQ 321 Mark
Which of the following numbers must be multiplied to $392$ to get a perfect cube?
View full question & answer→MCQ 331 Mark
A natural number is said to be a perfect cube, if it is the cube of some ________.
MCQ 341 Mark
Find the smallest number by which the number $392$ must be multiplied to obtain a perfect cube.
Answer$392 = 2 \times 2 \times 2 \times 7 \times 7 = 2^3 \times 7 \times 7.$
View full question & answer→MCQ 351 Mark
The one’s digit of the cube of the number $249$ is:
Answer$9 \times 9 \times 9 = 729.$
View full question & answer→MCQ 361 Mark
The one’s digit of the cube of the number $144$ is:
Answer$4 \times 4 \times 4 = 64.$
View full question & answer→MCQ 371 Mark
Mark $(\checkmark)$ against the correct answer: By what least number should $324$ be multiplied to get a perfect cube?
Answer$\begin{array}{c|c}2&324\\\hline2&162\\\hline3&81\\\hline3&27\\\hline3&9\\\hline3&3\\\hline&1\end{array}$
$324=2\times2\times3\times3\times3\times3$
$=2\times2\times3\times(3)^3$
Therefore, to show that the given number is the product of three triplets, we need to multiply $324$ by $(2 \times 3 \times 3)$.
In other words, we need to multiply $324$ by $18$ to make it a perfect cube
View full question & answer→MCQ 381 Mark
Which of the following is a perfect cube?
- A
$10000$
- B
$243$
- ✓
$343$
- D
$270000$
Answer$343$ is a Perfect Cube Number,
It is cube of $7$
$7^3 = 7 \times 7 \times 7 = 343$
View full question & answer→MCQ 391 Mark
By what number should we divide $135$ to get a perfect cube?
Answer$135 = 3 \times 3 \times 3 \times 5$
We can see, $5$ is the extra number which cannot be paired in a group of $3$.
Hence, $\frac{135}{5}=27$
View full question & answer→MCQ 401 Mark
What is the one’s digit in the cube root of the cube number $4913$?
Answer$7 \times 7 \times 7 = 343.$
View full question & answer→MCQ 411 Mark
Find the smallest number by which the number $250$ must be divided to obtain a perfect cube.
Answer$250 = 5 \times 5 \times 5 \times 2 = 5^3 \times 2.$
View full question & answer→MCQ 421 Mark
Cube root of $15625$ is:
Answer$15625 = 5 \times 5 \times 5 \times 5 \times 5 \times 5$
$\sqrt[3]{15625}=5\times5=25$
View full question & answer→MCQ 431 Mark
What will be the unit digit of the cube of a number ending with $6$?
View full question & answer→MCQ 441 Mark
What is the one’s digit in the cube root of the cube number $2744?$
Answer$4 \times 4 \times 4 = 64.$
View full question & answer→MCQ 451 Mark
Find the smallest number by which the following number must be divided to obtain a perfect cube. $135$
AnswerFactorizationof $135$
$135 = 3 \times 3 \times 3 \times 5$
$= 3^3 \times 5$
View full question & answer→MCQ 461 Mark
The length of each side of the cubical box is $2.4m.$ Its volume is:
- ✓
$13.824 cu.\ m$
- B
$13.824 cu.\ cm$
- C
$13.824\ cm^2$
- D
AnswerCorrect option: A. $13.824 cu.\ m$
$13.824 cu.\ m$
View full question & answer→MCQ 471 Mark
The cube of $0.9$ is:
AnswerCorrect option: A. $0.729$
$0.729$
View full question & answer→MCQ 481 Mark
The number of zeroes at the end of the cube root of the cube number $1000$ is:
Answer$\because$ Number of zeroes at the end of the cube $= 3$
$\therefore$ Number of zeroes at the end of the cube root $=\frac{3}{4}=1$
View full question & answer→MCQ 491 Mark
The cube of the given number is :$1.3.$
- ✓
$2.197$
- B
$2.187$
- C
$3.477$
- D
$8.447$
AnswerCorrect option: A. $2.197$
Cube of the number $1.3:$
$(1.3)^3=1.3 \times 1.3 \times 1.3 = 2.197.$
Hence, option $A$ is correct.
View full question & answer→MCQ 501 Mark
The smallest number that can be expressed the sum of two cubes in two different ways is:
- A
$20683$
- B
$13832$
- C
$4104$
- ✓
$1729$
AnswerCorrect option: D. $1729$
$20683=10^3+27^3=19^3+24^3 $
$ 13832=20^3+18^3=24^3+2^3 $
$ 4104=2^3+16^3=9^3+15^3 $
$ 1729=10^3+9^3 12^3+1^3$
View full question & answer→MCQ 511 Mark
What is the one’s digit in the cube root of the cube number $1728$?
Answer$2 \times 2 \times 2 = 8.$
View full question & answer→MCQ 521 Mark
Ratan made a cuboidal box length breadth and height of the cuboid are $10\ cm. 15\ cm.$ and $10\ cm$. How many cuboids will be need make a perfect cube?
AnswerVolume of the cuboidal box
$= 10 \times 10 \times 10 = 2 \times 5 \times 3 \times 5 \times 2 \times 5$
$= 5 \times 5 \times 5 \times 2 \times 2 \times 3$
There are two $2 's$ and one $3$ in the prime factorization.
Therefore, he need $2 \times 2 \times 3 = 18$ cuboids to make a perfect cube.
View full question & answer→MCQ 531 Mark
By what least number must $21600$ be multiplied to make it a perfect cube?
View full question & answer→MCQ 541 Mark
Which of the following numbers is a perfect cube?
MCQ 551 Mark
If a number is doubled then which of the following is a correct statement?
- A
Its cube is two times the cube of the given number.
- B
Its cube is three times the cube of the given number.
- C
Its cube is six times the cube of the given number.
- ✓
Its cube is eight times the cube of the given number.
AnswerCorrect option: D. Its cube is eight times the cube of the given number.
suppose we will take the no. $2$
If we double it, it becomes $4$
Cube of $2$ is $8$ and cube of $4$ is $64$
We will divide cubes of both numbers $ =\frac{64}{8} = 8$
So, it becomes eight times.
View full question & answer→MCQ 561 Mark
Which of the following is a perfect cube?
Answer$125 = 5 \times 5 \times 5 = 5^3$
View full question & answer→MCQ 571 Mark
The smallest natural number by which $36$ must be multiplied to get a perfect cube is _____.
AnswerPrime factorising $36$, we get,
$36 = 2 \times 2 \times 3 \times 3 = 2^2 \times 3^2.$
We know, a perfect cube has multiples of $3$ as powers of prime factors.
Here, number of $2'$s is $2$ and number of $3'$s is $2.$
So we need to multiply another $2$ and $3$ in the factorization to make $36$ a perfect cube.
Hence, the smallest number by which $36$ must be multiplied to obtain a perfect cube is $2 \times 3 = 6.$
Hence, option $A$ is correct.
View full question & answer→MCQ 581 Mark
Which of the following numbers is a cube number?
- ✓
$1000$
- B
$400$
- C
$100$
- D
$600$
AnswerCorrect option: A. $1000$
$1000$
View full question & answer→MCQ 591 Mark
What is the one’s digit in the cube root of the cube number $2197$?
Answer$3 \times 3 \times 3 = 27.$
View full question & answer→MCQ 601 Mark
Tick $(\checkmark)$ the correct answer:
$\sqrt[3]{125\times64}=\ ?$
Answer$\sqrt[3]{125\times64}$
$=\sqrt[3]{5\times5\times5\times4\times4\times4}$
$=\sqrt[3]{5^3\times4^3}$
$=5\times4$
$=20$
View full question & answer→MCQ 611 Mark
Two cubes have volume in the ratio $1 : 27$. The ratio of the area of the face of one to that of the other is:
- A
$1 : 3$
- B
$1 : 18$
- ✓
$1 : 9$
- D
$1 : 6$
AnswerCorrect option: C. $1 : 9$
$1 : 9$
View full question & answer→MCQ 621 Mark
Find the smallest number by which the number $1296$ must be divided to obtain a perfect cube:
Answer$1296 = 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3$
$= 2^3\times 2 \times 3^3× 3$
View full question & answer→MCQ 631 Mark
Find the smallest number by which the number $36$ must be multiphed to obtain a perfect cube.
Answer$36 = 2 \times 2 \times 3 \times 3.$
View full question & answer→MCQ 641 Mark
If the digit in one’s place of a number is $2,$ then the last digit of its cube will be:
AnswerIf the digit in one's place of a number is a, then the last digit of its cube will be the last digit of its cube.
Thus, if the digit in one's place of a number is $2,$ then the last digit of its cube will be unit digit of.
We know, the cube of $2,$ i.e. $2^3 = 8,$
Since the last digit of cube of $2$ is $8.$
View full question & answer→MCQ 651 Mark
Cube root of $512$ is:
AnswerBy prime factorisation, we get:
$512 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$
$\sqrt[3]{512}=2\times2\times2\times=8$
View full question & answer→MCQ 661 Mark
The smallest number by which $8788$ must be divided so that the quotient is a perfect cube is:
View full question & answer→MCQ 671 Mark
Which of the following the cube root of $- \frac{125}{512}$?
- A
$-\frac{5}{6}$
- B
$-\frac{8}{5}$
- C
$\frac{5}{8}$
- ✓
$-\frac{5}{8}$
AnswerCorrect option: D. $-\frac{5}{8}$
The given fraction is $-\frac{125}{512}$
It can be expressed as:
$-\frac{125}{512}=-\frac{5}{8}\times\frac{5}{8}\times\frac{5}{8}$
View full question & answer→MCQ 681 Mark
What is the one’s digit in the cube root of the cube number $1000000$?
Answer$0 \times 0 \times 0 = 0.$
View full question & answer→MCQ 691 Mark
The one’s digit of the cube of the number $50$ is:
Answer$0 \times 0 \times 0 = 0.$
View full question & answer→MCQ 701 Mark
Which of the following is equal to its own cube?
Answer$(-1)^3 = (-1) \times (-1) \times (-1) = -1$
$(-2)^3 = (-2) \times (-2) \times (-2) = -8$
$(-3)^3 = (-3) \times (-3) \times (-3) = -27$
$(-9)^3 = (-9) \times (-9) \times (-9) = -729$
View full question & answer→MCQ 711 Mark
How many digits will be there in the cube root of $512$?
View full question & answer→MCQ 721 Mark
Which of the following statement is true about cube number?
- ✓
Cube of negative numbers is negative.
- B
Cube of negative numbers is positive.
- C
Cube of negative number is either negative positive.
- D
Cube of positive numbers negative.
AnswerCorrect option: A. Cube of negative numbers is negative.
As we know that negative number times a negative number gives a positive number and positive number times a negative number gives a negative number.
Example: $(-5)^3 = -5 \times -5 \times -5 = -125$
View full question & answer→MCQ 731 Mark
There is no perfect cube which ends with $8.$
AnswerWe know, cube of $2$, i.e. $2^3= 8.$
Here, $8$ is a perfect cube.
That is, there is at least one perfect cube which ends with $8.$
Hence, the given statement is false.
Therefore, option $B$ is correct.
View full question & answer→MCQ 741 Mark
Which of the following are the cubes of odd natural numbers?
- A
$4096$
- B
$32768$
- ✓
$6859$
- D
$1728$
AnswerCorrect option: C. $6859$
View full question & answer→MCQ 751 Mark
Choose the correct statement:
- A
Cubes of odd natural numbers are odd.
- B
Cubes of even natural numbers are even.
- C
Cubes of negative integers are negative.
- ✓
View full question & answer→MCQ 761 Mark
If $72K$ is a perfect cube, then the value of $K$ is:
View full question & answer→MCQ 771 Mark
What is the one’s digit in the cube root of the cube number $4096$?
Answer$6 \times 6 \times 6 = 216.$
View full question & answer→MCQ 781 Mark
The one’s digit of the cube of the number $111$ is:
View full question & answer→MCQ 791 Mark
Find the cube of $0.6$.
- ✓
$0.216$
- B
$0.36$
- C
$21.6$
- D
$2.16$
AnswerCorrect option: A. $0.216$
Cube of $0.6$ is:
$(0.6)3 = 0.6 × 0.6 × 0.6$
$= 0.216.$
Hence, option $A$ is correct.
View full question & answer→MCQ 801 Mark
Find the smallest number by which the number $108$ must be multiplied to obtain a perfect cube.
Answer$108 = 2 \times 2 \times 3 \times 3 \times 3 = 2 \times 2 \times 3^3.$
View full question & answer→MCQ 811 Mark
Which is the smallest natural number by which $243$ must be multiplied to make the product a perfect cube?
Answer$243 \times 3 = 729$
Hence, by prime factorisation of $729$ we get
$729 = 3 \times 3 \times 3 \times 3 \times 3 \times 3$
$729 = 3^3 \times 3^3$
Taking cube root on both the sides, we get
$(729) = 3 \times 3 = 9$
View full question & answer→MCQ 821 Mark
Tick $(\checkmark)$ the correct answer: $\sqrt[3]{\frac{64}{343}}=\ ?$
- A
$\frac{4}{9}$
- ✓
$\frac{4}{7}$
- C
$\frac{4}{9}$
- D
$\frac{4}{9}$
AnswerCorrect option: B. $\frac{4}{7}$
$\sqrt[3]{\frac{64}{343}}$
$=\sqrt[3]{\frac{4\times4\times4}{7\times7\times7}}$
$=\sqrt[3]{\frac{4^3}{7^3}}$
$=\frac{4}{7}$
View full question & answer→MCQ 831 Mark
Find the smallest number by which the number $375$ must be divided to obtain a perfect cube.
Answer$375 = 3 \times 5 \times 5 \times 5 = 3 \times 5^3.$
View full question & answer→MCQ 841 Mark
If a number is tripled, then which of the following statement is correct?
AnswerCorrect option: C. Its cube is $27$ times the cube of the given number.
Let the given number be 'a
When the number is $18$ tripled it will become $3a$
Its cube will become $(3a)^3 = 27a^3$
The ratio of the cube of the original number to the cube of the number formed on the tripling will be $1 : 2$
View full question & answer→MCQ 851 Mark
The value of $\sqrt[3]{343}$ is:
View full question & answer→MCQ 861 Mark
The cube of an odd natural number is:
MCQ 871 Mark
Tick $(\checkmark)$ the correct answer: $\sqrt[3]{\frac{-512}{729}}=\ ?$
- A
$\frac{-7}{9}$
- ✓
$\frac{-8}{9}$
- C
$\frac{7}{9}$
- D
$\frac{8}{9}$
AnswerCorrect option: B. $\frac{-8}{9}$
$\sqrt[3]{\frac{-512}{729}}$
$\begin{array}{c|c}8&512\\\hline8&64\\\hline8&8\\\hline&1\end{array}$
$\begin{array}{c|c}9&729\\\hline9&81\\\hline9&9\\\hline&1\end{array}$
$=\sqrt[3]{\frac{(-8)\times(-8)\times(-8)}{9\times9\times9}}$
$=\sqrt[3]{\frac{(-8)^3}{(9)^3}}$
$=\frac{-8}{9}$
View full question & answer→MCQ 881 Mark
The number of zeroes at the end of the cube root of the cube number $8000000$ is:
Answer$\because $ Number of zeroes at the end of the cube $= 6$
$\therefore$ Number of zeroes at the end of the cube root $=\frac{6}{3}=2.$
View full question & answer→MCQ 891 Mark
Which of the following numbers is not a cube number?
- ✓
$10000$
- B
$3125$
- C
$64$
- D
$729$
AnswerCorrect option: A. $10000$
$10000 = 2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 5 \times 5.$
$= 2^4\times 5^4 = 23 \times 2 \times 5^3 \times 5.$
View full question & answer→MCQ 901 Mark
The number of zeroes at the end of the cube of the number $20$ is:
Answer$\because$ Number of zeroes at the end of the number $20 = 1$
$\therefore$ Number of zeroes at the end of its cube $= 3 \times 1 = 3.$
View full question & answer→MCQ 911 Mark
What is the one’s digit in the cube root of the cube number $6859?$
Answer$9 \times 9 \times 9 = 729.$
View full question & answer→MCQ 921 Mark
The one’s digit of the cube of the number $325$ is:
Answer$5 \times 5 \times 5 = 125.$
View full question & answer→MCQ 931 Mark
The one’s digit of the cube of the number $242$ is:
Answer$2 \times 2 \times 2 = 8.$
View full question & answer→MCQ 941 Mark
Which of the following numbers is not a perfect cube?
- A
$1331$
- B
$512$
- C
$343$
- ✓
$100$
Answer$100 = 2 \times 2 \times 5 \times 5 = 2^2\times 5^2 $
View full question & answer→MCQ 951 Mark
Which of the following is correct?
- A
Cube of a negative number is always positive.
- ✓
Cube of a negative number is always negative.
- C
Cube of a negative number may be positive or negative.
- D
AnswerCorrect option: B. Cube of a negative number is always negative.
Multiplication of three negative numbers (i.e. the cube), will always be negative.
Eg: $(-4)^3$
$= -4 \times -4 \times -4$
$= 16 \times -4 = -64,$ which is negative.
View full question & answer→MCQ 961 Mark
The one’s digit of the cube of the number $123$ is:
Answer$3 \times 3 \times 3 = 27.$
View full question & answer→MCQ 971 Mark
The one’s digit of the cube of the number $68$ is:
Answer$8 \times 8 \times 8 = 512.$
View full question & answer→MCQ 981 Mark
How many cuboids of dimensions $15\ cm, 30\ cm,15\ cm$ will be needed to form a cube?
View full question & answer→MCQ 991 Mark
Tick $(\checkmark)$ the correct answer: Which of the following numbers is a perfect cube?
Answer$A.$ $141$
$= 3 \times 47$
$\begin{array}{c|c}3&141\\\hline47&47\\\hline&1\end{array}$
$B.$ $294$
$= 2 \times 7 \times 7 \times 3$
$\begin{array}{c|c}2&294\\\hline7&147\\\hline7&21\\\hline3&3\\\hline&1\end{array}$
$C.$ $216$
$= 2 \times 2 \times 2 \times 3 \times 3 \times 3$
$= 2^3 \times 3^3$
$\begin{array}{c|c}2&216\\\hline2&108\\\hline2&54\\\hline3&27\\\hline3&9\\\hline3&3\\\hline&1\end{array}$
$D.$ $496$
$= 2 \times 2 \times 2 \times 2 \times 31$
$\begin{array}{c|c}2&496\\\hline2&248\\\hline2&124\\\hline2&62\\\hline31&31\\\hline&1\end{array}$
We see that $216$ is a perfect cube.
View full question & answer→MCQ 1001 Mark
Tick $(\checkmark)$ the correct answer: $\sqrt[3]{512}=\ ?$
Answer$\sqrt[3]{512}$
$\begin{array}{c|c}2&152\\\hline2&256\\\hline2&128\\\hline2&64\\\hline2&32\\\hline2&16\\\hline2&8\\\hline2&4\\\hline2&2\\\hline&1\end{array}$
$=\sqrt[3]{2\times2\times2\times2\times2\times2\times2\times2\times2}$
$=\sqrt[3]{2^3\times2^3\times2^3}$
$=2\times2\times2$
$=8$
View full question & answer→MCQ 1011 Mark
The cube of the given number is $: 0.4.$
- ✓
$0.064$
- B
$0.074$
- C
$0.194$
- D
AnswerCorrect option: A. $0.064$
Cube of the number $0.4:$
$(0.4)^3 = 0.4 \times 0.4 \times 0.4 = 0.064.$
Hence, option $A$ is correct.
View full question & answer→MCQ 1021 Mark
Find the smallest number by which the number $88$ must be divided to obtain a perfect cube.
Answer$88 = 2 \times 2 \times 2 \times 11 = 2^3 \times 11.$
View full question & answer→MCQ 1031 Mark
The cube root of $13824$ is __________.
View full question & answer→MCQ 1041 Mark
Find the smallest number by which the number $72$ must be multiplied to obtain a perfect cube.
Answer$72 = 2 \times 2 \times 2 \times 3 \times 3 = 2^3\times 3 \times 3.$
View full question & answer→MCQ 1051 Mark
How many perfect cubes are there between $1$ and $100?$
AnswerFinding all the perfect cubes between $1$ and $100$ we get,
$(2)^3 = 2 \times 2 \times 2 = 8$
$(3)^3 = 3 \times 3 \times 3 = 27$
$(4)^3 = 4 \times 4 \times 4 = 64$
$(5)^3 = 5 \times 5 \times 5 = 125$
Now, $125$ is more than $100$ which doesn't Satisfies the condition given in the question.
Therefore, there are $3$ perfect cubes between $1$ and $100.$
View full question & answer→MCQ 1061 Mark
A number raised to power $3$ is called the _____.
- ✓
- B
- C
- D
Square root of that number
AnswerIf a number is raised to the power $3$, then it is called the cube of that number.
Hence, option $A$ is correct.
View full question & answer→MCQ 1071 Mark
Find the smallest number by which the following number must be multiplied to obtain a perfect cube : $243$
AnswerPrime factorizing $243,$ we get,
$243 = 3 \times 3 \times 3 \times 3 \times 3 = 3^5.$
We know, a perfect cube has multiples of $3$ as powers of prime factors.
Here, number of $3'$s is $5.$
So we need to multiply another $3$ in the factorization to make $243$ a perfect cube.
Hence, the smallest number by which $243$must be multiplied to obtain a perfect cube is $3.$
Therefore, option $A$ is correct.
View full question & answer→MCQ 1081 Mark
Mark $(\checkmark)$ against the correct answer: $\Big(1\frac{3}{4}\Big)^3=\ ?$
- A
$1\frac{27}{64}$
- B
$2\frac{27}{64}$
- ✓
$5\frac{23}{64}$
- D
AnswerCorrect option: C. $5\frac{23}{64}$
$\Big(1\frac{3}{4}\Big)^3=\Big(\frac{7}{4}\Big)^3$
$=\frac{(7)^3}{(4)^3}$
$=\frac{7\times7\times7}{4\times4\times4}$
$=\frac{343}{64}$
$\Big(1\frac{3}{4}\Big)^3=\frac{343}{64}=5\frac{23}{64}$
$\therefore\Big(1\frac{3}{4}\Big)^3=5\frac{23}{64}$
View full question & answer→MCQ 1091 Mark
The cube of even numbers is always:
AnswerThe cube of even number is always even as an even number times
an even number is always an even number.
For Example: $2 \times 2 \times 2 = 8$
View full question & answer→MCQ 1101 Mark
Find the smallest number by which the number $200$ must be multiplied to obtain a perfect cube.
Answer$200 = 2 \times 2 \times 2 \times 5 \times 5 = 2^3\times 5 \times 5.$
View full question & answer→MCQ 1111 Mark
Which of the following is a perfect cube?
- ✓
$125$
- B
$135$
- C
$145$
- D
$115$
View full question & answer→MCQ 1121 Mark
Mark $(\checkmark)$ against the correct answer: Which of the following is a cube of an odd number?
- A
$216$
- B
$512$
- ✓
$343$
- D
$1000$
AnswerThe cube of an odd number will always be an odd number.
Therefore, $343$ is the cube of an odd number.
View full question & answer→MCQ 1131 Mark
By what number should $81$ be divided to get a perfect cube?
AnswerThe prime factorisation of $81$ will be:
$81 = 3 \times 3 \times 3 \times 3$
$81 = 3^3 \times 3$
Hence, we need to divide $81$ by $3$ to get:
$\frac{81}{3}=27=3^3$
View full question & answer→MCQ 1141 Mark
The volume of a cube is $64\ cm³$ The edge of the cube is:
- ✓
$4\ cm$
- B
$8\ cm$
- C
$16\ cm$
- D
$6\ cm$
AnswerCorrect option: A. $4\ cm$
Edge $=\sqrt[3]{64}=\sqrt{2\times2\times2\times2\times2\times2}$
$=\sqrt[3]{2^3\times2^3}=2\times2=4$
View full question & answer→MCQ 1151 Mark
The number which is not a perfect cube among the following is:
- A
$512$
- B
$1331$
- C
$216$
- ✓
$243$
View full question & answer→MCQ 1161 Mark
What is the one’s digit in the cube root of the cube number $8000$?
Answer$0 \times 0 \times 0 = 0.$
View full question & answer→MCQ 1171 Mark
The cube root of $27^2$ is:
View full question & answer→MCQ 1181 Mark
Which of the following numbers is cube root of $64$?
View full question & answer→MCQ 1191 Mark
Tick $(\checkmark)$ the correct answer: By what least number should $1536$ be divided to get a perfect cube?
Answer$(A) 3$
Factorising $1536$,
We get,
$\begin{array}{c|c}2&1536\\\hline2&768\\\hline2&384\\\hline2&192\\\hline2&96\\\hline2&48\\\hline2&24\\\hline2&12\\\hline2&6\\\hline3&3\\\hline&1\end{array}$
$1536=2\times2\times2\times2\times2\times2\times2\times2\times2\times3$
$=2^3\times2^3\times2^3\times3$
We see that $3$ is left
$\therefore$ In order to get a perfect cube, we should divide it by $3$.
View full question & answer→MCQ 1201 Mark
Which of the following are the cubes of even natural numbers?
- A
$3375$
- ✓
$13824$
- C
$729$
- D
$1331$
AnswerCorrect option: B. $13824$
$13824$
View full question & answer→MCQ 1211 Mark
If the digit in the unit's place of a number is $7.$ what will be the digit at the unit's place in its cube?
AnswerLet us consider few examples.
Cube of $7$
$= 7^3 = 7 \times 7 \times 7 = 343$
Cube of $17$
$17^3 = 17 \times 17 \times 17 = 4913$
Cube of $27$
$27^3 = 27 \times 27 \times 27 = 19683$
From the above examples, we can see that cube of the numbers with
$7$ at the unit's place end, with $3$ at their unit's place.
View full question & answer→MCQ 1221 Mark
Mark $(\checkmark)$ against the correct answer: $\sqrt[3]{\frac{-343}{729}}=\ ?$
- A
$\frac{7}{9}$
- ✓
$\frac{-7}{9}$
- C
$\frac{-9}{7}$
- D
$\frac{9}{7}$
AnswerCorrect option: B. $\frac{-7}{9}$
By prime factorisation method
$\sqrt[3]{\frac{-343}{729}}$
$=\frac{\sqrt[3]{-343}}{\sqrt[3]{729}}$
$=\frac{\sqrt[3]{(-7)\times(-7)\times(-7)}}{\sqrt[3]{3\times3\times3\times3\times3\times3}}$
$=\frac{\sqrt[3]{(-7)^3}}{\sqrt[3]{(3)^3\times(3)^3}}$
$=\frac{\sqrt[3]{(-7)^3}}{\sqrt[3]{(9)^3}}$
$=\frac{-7}{9}$
$\therefore\sqrt[3]{\frac{-343}{729}}=\frac{-7}{9}$
View full question & answer→MCQ 1231 Mark
If the side of the cubical box is $9\ cm.$ What will be its volume?
- ✓
$729\ cm^3$
- B
$21\ cm^3$
- C
$343\ cm^3$
- D
$27\ cm^3$
AnswerCorrect option: A. $729\ cm^3$
The volume of the cubical box is given by:$ (side)^3$
The volume of the cubical box with side $9\ cm.$
$= (9cm)^3= 9cm \times 9cm \times 9\ cm = 729\ cm^3$
View full question & answer→MCQ 1241 Mark
What will be the unit digit of the cube of a number ending with $2$?
View full question & answer→MCQ 1251 Mark
The cube root of $0.001728$ is:
AnswerCorrect option: A. $0.12$
$0.12$
View full question & answer→MCQ 1261 Mark
The one’s digit of the cube of the number $326$ is:
Answer$6 \times 6 \times 6 = 216.$
View full question & answer→MCQ 1271 Mark
Which of the following is the cube root of $27000$?
AnswerCube root is the number which is obtained when a number is multiplied by itself two times.
The cube is basically the third power of a number and the cube root is that same number.
Given the cube root is $27000$.
If we multiply $30$ to itself two times we will get it's cube root.
Cube of $30$ i,e power of $3$ on $30$.
$30 \times 30 \times 30 = 27000$
Therefore the cube root is $30$.
View full question & answer→MCQ 1281 Mark
The smallest number by which $2560$ must be multiplied so that the product is a perfect cube is:
View full question & answer→MCQ 1291 Mark
The one's digit of the cube of $33$ is:
AnswerIt is known that, the cubes of the numbers ending with digits $3$, has $7$ at one's digit.
$\therefore$ The one's digit of the cube of $33$ is $7$.
View full question & answer→MCQ 1301 Mark
What is the cube of $0.8$?
- A
$51.2$
- B
$0.0512$
- C
$5.12$
- ✓
$0.512$
AnswerCorrect option: D. $0.512$
The cube of $0.8$ is given as:
$\big(0.8\big)^3=\Big(\frac{8}{10}\Big)^3 $
$=\frac{512}{1000}=0.512$
View full question & answer→MCQ 1311 Mark
Find the smallest number by which the following number must be divided to obtain a perfect cube.$192$
AnswerFactorizationof $192$
$192 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3$
$= 26 \times 3$
Tomakandapandrfandctcub e,w
eneedt ohavandmul tiples of $3$ apowersofprimefactors
,i. e,wedivi d e t h e n m be rby$3$
View full question & answer→MCQ 1321 Mark
How many small cubes with edges of $10\ cm$ can be just accommodated in a cubical box of $1\ m$ edge?
- ✓
$1000$
- B
$10$
- C
$10000$
- D
$100$
AnswerCorrect option: A. $1000$
$1000$
View full question & answer→MCQ 1331 Mark
Find the smallest number by which the number $128$ must be multiplied to obtain a perfect cube.
Answer$128 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$
$= 2^3 \times 2^3 \times 2.$
View full question & answer→MCQ 1341 Mark
The cube root of $216000$ is?
AnswerThe given number is $216000$.
It can be expressed as:
$216000=\sqrt[3]{216\times10^3}$
$=6\times10=60$
View full question & answer→MCQ 1351 Mark
What is the cube of $2a?$
- ✓
$8a^3$
- B
$16a^3$
- C
$2a^3$
- D
$4a^3$
AnswerCorrect option: A. $8a^3$
$(2a)^3 = 2a \times 2a \times 2a$
$= (2 \times 2 \times 2) \times (a \times a \times a)$
$= 8a^3$
View full question & answer→MCQ 1361 Mark
Which of these numbers is not a cube number?
- A
$343$
- B
$729$
- ✓
$10000$
- D
$64$
AnswerCorrect option: C. $10000$
By prime factorisation method.
$10000 = 2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 5 \times 5.$
$= 2^4 \times 5^4 = 2^3 \times 2 \times 5^3 \times 5$
View full question & answer→MCQ 1371 Mark
Which of the following is not a perfect cube?
- ✓
$243$
- B
$1331$
- C
$1000$
- D
$216$
Answer$243 = 3 \times 3 \times 3 \times 3 \times 3 = 3^3 \times 3^2$
View full question & answer→MCQ 1381 Mark
Cube of $(−2)$ is _______.
AnswerCube of $(-2)$ is:
$(-2)^3= (-2) \times (-2) \times (-2)$
$= -8.$
View full question & answer→MCQ 1391 Mark
The cube of a number is $8$ times the cube of another number. If the sum of the cubes of numbers is $243$, the difference of the numbers is:
View full question & answer→MCQ 1401 Mark
Which of the following is the cube root of $-\frac{64}{343}$?
- A
$\frac{7}{4}$
- B
$-\frac{7}{4}$
- C
$\frac{4}{7}$
- ✓
$-\frac{4}{7}$
AnswerCorrect option: D. $-\frac{4}{7}$
$-\frac{64}{343}$
$=-\frac{\sqrt[3]{64}}{\sqrt[3]{343}}$
$=-\frac{\sqrt[3]{4\times{4}\times{4}}}{\sqrt[3]{7\times{7}\times{7}}}$
$=-\frac{4}{7}$
View full question & answer→MCQ 1411 Mark
What is the volume of a cube whose each side is $4\ cm?$
- A
$24\ cm^3$
- B
$48\ cm^3$
- ✓
$64\ cm^3$
- D
$25\ cm^3$
AnswerCorrect option: C. $64\ cm^3$
$64cm^3$
View full question & answer→MCQ 1421 Mark
What is the one’s digit in the cube root of the cube number $3375$?
Answer$5 \times 5 \times 5 = 125.$
View full question & answer→MCQ 1431 Mark
The one’s digit of the cube of the number $242$ is:
View full question & answer→MCQ 1441 Mark
Find the smallest number by which the number $256$ must be divided to obtain a perfect cube.
Answer$256 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$
$= 2^3 \times 2^3 \times 2 \times 2$
View full question & answer→MCQ 1451 Mark
There is no perfect cube which ends with $8$.
AnswerWe know,
cube of $2$, i.e. $23 = 8,$ which is a perfect cube.
That is, there exists a perfect cube which ends in $8$.
Therefore, the given statement is false and option $B$ is correct.
View full question & answer→MCQ 1461 Mark
Apala makes a cuboid of plasticine of sides $5\ cm, 4\ cm, 2\ cm.$ How many such cuboids will be needed to form a cube?
Answer$Volume = 5 \times 4 \times 2 = 5 \times 2 \times 2 \times 2$
$= 5 \times 2^3.$
View full question & answer→MCQ 1471 Mark
The number of zeroes at the end of the cube of the number $100$ is:
Answer$\therefore$ Number of zeroes at the end of the number $100 = 2$
$\therefore$ Number of zeroes at the end of its cube $= 3 \times 2 = 6$.
View full question & answer→MCQ 1481 Mark
Find the cube root of the following number by prime factorisation method: $64$
AnswerPrime factorising, we get,
$64 = 2 \times 2 \times 2 \times 2 \times 2 \times 2$
$= 4 \times 4 \times 4.$
Here, the factor $4$ occur as triplet. Hence, it is a perfect cube.
Therefore, cube root of $64$, i.e. $\sqrt[3]{64}=4$
View full question & answer→MCQ 1491 Mark
If $15x^3 = 3240.$ Then what is the value of $x'$?
AnswerGiven $15x^3 = 3240$
$\Rightarrow\text{x}^3=\frac{3240}{15}= 3240 =216$
$\Rightarrow\text{x}=\sqrt[3]{216}$
$\Rightarrow\text{x}=6$
View full question & answer→MCQ 1501 Mark
Cube of any odd number is even.
AnswerWe know, cube of any odd number is odd.
Eg. The cube of the odd number $3$ is $27$, which is an odd number.
Hence, the given statement is false.
Therefore, option $B$ is correct.
View full question & answer→MCQ 1511 Mark
What is the one’s digit in the cube root of the cube number $1331$?
Answer$1 \times 1 \times 1 = 1.$
View full question & answer→MCQ 1521 Mark
If $\text{a}=\frac{1}{\sqrt[3]{\text{b}}}$ ,then $b$ is:
- A
$\text{a}^3$
- B
$\sqrt{a}$
- ✓
$\frac{1}{\text{a}^3}$
- D
$\sqrt[3]{a}$
AnswerCorrect option: C. $\frac{1}{\text{a}^3}$
Given $\text{a}=\frac{1}{\sqrt[3]{\text{b}}}$
$\Rightarrow \text{a}\frac{1}{(\text{b})^\frac{1}{3}}$
Cubing both the sides we get,
$\text{a}^3=\Bigg(\frac{1}{\text{b}^{\frac{1}{3}}}\Bigg)^3=\frac {1}{\text{b}}$
$\Rightarrow\text{b}=\frac{1}{\text{a}^3}$
View full question & answer→MCQ 1531 Mark
Which of the following numbers are perfect cubes?
- ✓
$343$
- B
$5324$
- C
$108$
- D
$243$
View full question & answer→MCQ 1541 Mark
Find the smallest number by which the number $121$ must be multiplied to obtain a perfect cube.
Answer$121 = 11 \times 11.$
View full question & answer→MCQ 1551 Mark
The three numbers are in the ratio $1 : 2 : 3$ the sum of their cubes is $26244.$ What are the numbers?
- A
$4, 8, 12$
- B
$7, 14, 21$
- C
$6, 12, 36$
- ✓
$9, 18, 27$
AnswerCorrect option: D. $9, 18, 27$
Let the numbers be $x, 2 x$ and $3 x$.
According to the given condition,
$(x)^3+(2 x)^3+(3 x)^3=26244 $
$\Rightarrow x^3+8 x^3+27 x^3=26244 $
$\Rightarrow 36 x^3=26244 $
$\Rightarrow x^3=729 $
$\Rightarrow x=\sqrt[3]{729}=9$
Therefore, $2 x=2 \times 9=18$ and $3 x=3 \times 9=27$
View full question & answer→MCQ 1561 Mark
The value of $3\sqrt{343}\times3\sqrt{-64}$ is:
View full question & answer→MCQ 1571 Mark
Which of the following numbers is a cube number?
- ✓
$1000$
- B
$400$
- C
$100$
- D
$600$
AnswerCorrect option: A. $1000$
$1000 = 10 \times 10 \times 10 = 10^3$
View full question & answer→MCQ 1581 Mark
The prime factorisation of $64$ is:
- A
$2 \times 2 \times 2$
- B
$4 \times 4 \times 4$
- C
$8 \times 8 \times 8$
- ✓
View full question & answer→MCQ 1591 Mark
What is the one’s digit in the cube root of the cube number $5832$?
Answer$8 \times 8 \times 8 = 512.$
View full question & answer→MCQ 1601 Mark
The cube of an odd natural number is:
Answer$3 \times 3 \times 3 = 27$ (odd).
View full question & answer→MCQ 1611 Mark
Tick $(\checkmark)$ the correct answer: $\Big(1\frac{3}{10}\Big)^3=\ ?$
- A
$1\frac{27}{1000}$
- B
$2\frac{27}{1000}$
- ✓
$2\frac{197}{1000}$
- D
AnswerCorrect option: C. $2\frac{197}{1000}$
$\Big(1\frac{3}{10}\Big)^3$
$=\Big(\frac{13}{10}\Big)^3$
$=\frac{13\times13\times13}{10\times10\times10}$
$=\frac{2197}{1000}$
$=2\frac{197}{1000}$
View full question & answer→MCQ 1621 Mark
The cube root of $1.331$ is:
- A
$11$
- B
$0.011$
- ✓
$1.1$
- D
$0.11$
View full question & answer→MCQ 1631 Mark
Find the cube of $75$.
- ✓
$421875$
- B
$400175$
- C
$5625$
- D
AnswerCorrect option: A. $421875$
$421875$
View full question & answer→MCQ 1641 Mark
A natural number is said to be a perfect cube, if it is the cube of some _________.
MCQ 1651 Mark
Cube of an odd natural number is an _____ number.
AnswerWe know, the multiplication of odd natural numbers $3$ times, i.e. the cube of an odd natural number, will always be odd.
That is because an odd number multiplied to another odd number, always yields an odd number.
For example, consider the odd natural numbers $3$ and $5$.
Then, their cube is $33 = 27$ and $53 = 125$, whose units place is odd.
That is, the cubes are also odd.
Hence, the cube of an odd natural number is an odd number.
View full question & answer→MCQ 1661 Mark
The smallest number by which $392$ must be multiplied so that the product is a perfect cube is:
View full question & answer→MCQ 1671 Mark
The cube of $23$ is ___________
- A
$2304$
- B
$23$
- ✓
$12167$
- D
$529$
AnswerCorrect option: C. $12167$
$12167$
View full question & answer→MCQ 1681 Mark
The value of $4\sqrt[3]{1000}$ is:
Answer$4\sqrt[3]{1000}=4\sqrt[3]{(10\times10\times10)}=4\times10=40$
View full question & answer→MCQ 1691 Mark
Find the smallest number by which the number $200$ must be multiplied to obtain a perfect cube.
AnswerThe prime factorisation of $200$ gives
$200 = 2 \times 2 \times 2 v\times 5 \times 5 = 2^3 \times 5 \times 5$
Now multiply by $5$ on both sides.
$200 \times 5 = 2^3 \times 53$
$\big(1000\big)\frac{1}{3}=2\times5=10$
View full question & answer→MCQ 1701 Mark
Find the cube root of the following number by prime factorisation method : $512$
AnswerPrime factorising, we get,
$512 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$
$= 8 \times 8 \times 8.$
Here, the factor $8$ occur as triplet. Hence, it is a perfect cube.
Therefore, cube root of $512$, i.e. $\sqrt[3]{512}=8$
View full question & answer→MCQ 1711 Mark
The cube of $23$ is:
- A
$2304$
- B
$529$
- C
$23$
- ✓
$12167$
AnswerCorrect option: D. $12167$
Cube of $23 = 23 \times 23 \times 23 = 12167$
View full question & answer→MCQ 1721 Mark
The smallest natural number by which $243$ must be multiplied to make the product a perfect cube is __________.
View full question & answer→MCQ 1731 Mark
Which of the following numbers is a perfect cube?
MCQ 1741 Mark
Which of the following numbers must be subtracted from $345$ to get a perfect cube?
View full question & answer→MCQ 1751 Mark
Mark $(\checkmark)$ against the correct answer: $\frac{\sqrt[3]{128}}{\sqrt[3]{250}}=\ ?$
- A
$\frac{3}{5}$
- ✓
$\frac{4}{5}$
- C
$\frac{2}{5}$
- D
AnswerCorrect option: B. $\frac{4}{5}$
Resolving the numerator and the denominator into prime factors:
$\frac{\sqrt[3]{128}}{\sqrt[3]{250}}$
$=\sqrt[3]{\frac{128}{250}}$
$=\sqrt[3]{\frac{2\times8\times8}{2\times5\times5\times5}}$
$=\sqrt[3]{\frac{\not{2}\times8\times8}{\not{2}\times5\times5\times5}}$
$=\sqrt[3]{\frac{8\times8}{5\times5\times5}}$
$=\sqrt[3]{\frac{(2)^3\times(2)^3}{(5)^3}}$
$=\frac{2\times2}{5}$
$=\frac{4}{5}$
View full question & answer→MCQ 1761 Mark
Find the ones digit of cube root of $2197$.
View full question & answer→MCQ 1771 Mark
Tick $(\checkmark)$ the correct answer: Which of the following numbers is a perfect cube?
- A
$1152$
- ✓
$1331$
- C
$2016$
- D
$739$
AnswerCorrect option: B. $1331$
$A.$ $1152$
$= 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3$
$= 2^3 \times 2^3 \times 3^2$
$\begin{array}{c|c}2&1152\\\hline2&576\\\hline2&288\\\hline2&144\\\hline2&72\\\hline2&36\\\hline2&18\\\hline3&9\\\hline3&3\\\hline&1\end{array}$
$B.$ $1131$
$= 11 \times 11 \times 11$
$= (11)^3$
$\begin{array}{c|c}11&1331\\\hline11&121\\\hline11&11\\\hline&1\end{array}$
$C.$ $2016$
$= 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 7$
$= 2^3 \times 2 \times 2 \times 3 \times 3 \times 7$
$\begin{array}{c|c}2&2016\\\hline2&1008\\\hline2&504\\\hline2&252\\\hline2&126\\\hline3&63\\\hline3&21\\\hline7&7\\\hline&1\end{array}$
$D.$ $739$
$= 1 \times 739$
We see that $1331$ is a perfect cube.
View full question & answer→MCQ 1781 Mark
What should be divided by $53240$ to make it a perfect cube?
AnswerThe prime factorisation of $53240$
$53240 = 2 \times 2 \times 2 \times 11 \times 11 \times 11 \times 5 = 2^3 \times 11^3 \times 5$
Hence, we need to divide $53240$ by $5$
$\frac{53240}{5}=10648$ is a perfect cube.
View full question & answer→MCQ 1791 Mark
Which among the following is a perfect cube?
- A
$400$
- ✓
$15625$
- C
$243$
- D
$9000$
AnswerCorrect option: B. $15625$
$400 = 2 \times 2 \times 2 \times 2 \times 5 \times 5; 2 \times 5 \times 5$ remains after grouping into triplets.Therefore, it is not a perfect square.
$15625 = 5 \times 5 \times 5 \times 5 \times 5 \times 5$ In this factorization, nothing remains after grouping $S'$s in triplets. Therefore, it is a perfect square.
$243 = 3 \times 3 \times 3 \times 3 \times 3$ In this factorization $3 \times 3$ remains after grouping $3'$ in triplets. Hence, it is not a perfect square.
$9000 = 3 \times 3 \times 2 \times 2 \times 2 \times 5 \times 5 \times 5$ In this factorization $3 \times 3$ remains after groping $5's$ and $2's$ in triplets.
Hence, it is not a perfect. Square.
View full question & answer→MCQ 1801 Mark
The one’s digit of the cube of the number $347$ is:
Answer$7 \times 7 \times 7 = 343.$
View full question & answer→MCQ 1811 Mark
Which among is the smallest number by which we should multiply $6125$ to get a perfect cube?
AnswerThe prime factorization of $6125$ is:$ 5 \times 5 \times 5 \times 7 \times 7$
Here the prime factor $7$ does not appear in a group of three. To make it a perfect number, we need one more $7$
In that case $6125 \times 7 = 5 \times 5 \times 5 \times 7 \times 7 = 42875$ which is a perfect cube.
View full question & answer→MCQ 1821 Mark
What will be the unit digit of $\sqrt[3]{216}$ ?
View full question & answer→MCQ 1831 Mark
If $8^{3}=512,$ then $\sqrt[3]{512}=$
View full question & answer→MCQ 1841 Mark
If $7^{3}=343,$ then $\sqrt[3]{343}=$
View full question & answer→MCQ 1851 Mark
How many zeros will be there in the cube root of $800$?
View full question & answer→MCQ 1861 Mark
How many zeros will be there in the cube root of $27000$?
View full question & answer→MCQ 1871 Mark
What will be the unit digit of $\sqrt[3]{15625} ?$
View full question & answer→MCQ 1881 Mark
How many digits will be there in the cube root of $512$?
View full question & answer→MCQ 1891 Mark
How many digits will be there in the cube root of $46656$?
View full question & answer→MCQ 1901 Mark
The number of digits in the cube root of a $6$-digit number is _______ .
View full question & answer→MCQ 1911 Mark
$9$ is the cube root of __________ .
View full question & answer→MCQ 1921 Mark
What will be the unit digit of the cube root of a number ends with 7?
MCQ 1931 Mark
What will be the unit digit of the cube root of a number ends with $3$?
View full question & answer→MCQ 1941 Mark
What will be the unit digit of the cube root of a number ends with $2$?
View full question & answer→MCQ 1951 Mark
What will be the unit digit of the cube root of a number ends with $8$?
View full question & answer→MCQ 1961 Mark
If the volume of a cube is $125\ cm^3$ then what would be the length of its side?
View full question & answer→MCQ 1971 Mark
Which of the following is true for any natural number $n$?
- A
$n^{2}>n^{3}$
- ✓
$n^{3}>n^{2}$
- C
$n^{2}=n^{3}$
- D
AnswerCorrect option: B. $n^{3}>n^{2}$
$n^{3}>n^{2}$
View full question & answer→MCQ 1981 Mark
The value of $\sqrt[3]{343}$ is
View full question & answer→MCQ 1991 Mark
The cube root of $512$ is ________ .
View full question & answer→MCQ 2001 Mark
The symbol for cube root is
- A
$\sqrt{3}$
- ✓
$\sqrt[3]{\square}$
- C
$\sqrt{3}$
- D
$\sqrt[2]{3}$
AnswerCorrect option: B. $\sqrt[3]{\square}$
$\sqrt[3]{\square}$
View full question & answer→MCQ 2011 Mark
What is the volume of a cube whose edge is $2\ cm$?
View full question & answer→MCQ 2021 Mark
Which of the following is a perfect cube?
MCQ 2031 Mark
$729$ is the value of
- A
$8^{3}$
- ✓
$9^{3}$
- C
$6^{3}$
- D
$4^{3}$
AnswerCorrect option: B. $9^{3}$
$9^{3}$
View full question & answer→MCQ 2041 Mark
How many cuboids of dimensions $15\ cm, 30\ cm ,15\ cm$ will be needed to form a cube?
View full question & answer→MCQ 2051 Mark
A cuboid has dimensions $5\ cm , 2\ cm, 5\ cm$ .How many such cuboid will be needed to form a cube?
View full question & answer→MCQ 2061 Mark
What will be the unit digit of the cube of a number ending with $6$?
View full question & answer→MCQ 2071 Mark
What will be the unit digit of the cube of a number ending with $4$?
View full question & answer→MCQ 2081 Mark
What will be the unit digit of the cube of a number ending with $2$?
View full question & answer→MCQ 2091 Mark
The expansion of $\mathrm{a}^{3}$ is
- A
$3 \times a$
- B
$a+a+a$
- C
$3 \times 3 \times 3$
- ✓
$a \times a \times a$
AnswerCorrect option: D. $a \times a \times a$
$a \times a \times a$
View full question & answer→MCQ 2101 Mark
The smallest natural number by which $135$ must be divided to obtain a perfect cube is
View full question & answer→MCQ 2111 Mark
The smallest natural number by which $704$ must be divided to obtain a perfect cube is
View full question & answer→MCQ 2121 Mark
The smallest natural number by which $243$ must be multiplied to make the product a perfect cube is __________ .
View full question & answer→MCQ 2131 Mark
By which smallest natural number $392$ must be multiplied so as to make the product a perfect cube?
View full question & answer→MCQ 2141 Mark
Which of the following is Hardy-Ramanujan Number?
- A
$1724$
- B
$1725$
- C
$1727$
- ✓
$1729$
AnswerCorrect option: D. $1729$
$1729$
View full question & answer→MCQ 2151 Mark
Each prime factor appears _________ times in its cube?
MCQ 2161 Mark
The cube of an odd number is always __________ .
MCQ 2171 Mark
The cube of an even number is always ____________ .
MCQ 2181 Mark
The value of $5^{3}$ is __________ .
View full question & answer→MCQ 2191 Mark
The cube of $4$ is _______________ .
View full question & answer→MCQ 2201 Mark
Which of the following is not a perfect cube?
MCQ 2211 Mark
Cube root of $15625$ is:
Answer$15625=5 \times 5 \times 5 \times 5 \times 5 \times 5$ $^3 \sqrt{15625}=5 \times 5=25$
View full question & answer→MCQ 2221 Mark
A perfect cube does not end with _____ zeros.
Answer$10^{3}=1000$ $20^{3}=8000$ $30^{3}=27000$
View full question & answer→MCQ 2231 Mark
The value of $4^{3} \sqrt{1000 \text { is: }}$
Answer$\left.4^{3} \sqrt{1000}=4^{3} \sqrt{(} 10 \times 10 \times 10\right)=4 \times 10=40$
View full question & answer→MCQ 2241 Mark
What should be divided by $53240$ to make it a perfect cube?
Answer$53240=2 \times 2 \times 2 \times 11 \times 11 \times 11 \times 5=2^{3} \times 11^{3} \times 5$
Hence, we need to divide $53240$ by $5$. $53240 / 5=10648$ is a perfect cube.
View full question & answer→MCQ 2251 Mark
Cube root of $512$ is:
AnswerBy prime factorisation we get: $512=2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$
$^3 \sqrt{5} 12=2 \times 2 \times 2=8$
View full question & answer→MCQ 2261 Mark
By what number should we divide $135$ to get a perfect cube?
Answer$135 = 3 x 3 x 3 x 5$ We can see, $5$ is the extra number which cannot be paired in a group of $3$. Hence, $135/5 = 27$
View full question & answer→MCQ 2271 Mark
By what number should 81 be divided to get a perfect cube?
AnswerThe prime factorisation of 81 will be: $81=3 \times 3 \times 3 \times 3$ $81=3^{3} \times 3$ Hence, we need to divide $81$ by $3$ to get: $81 / 3=27=3^{3}$
View full question & answer→MCQ 2281 Mark
Which of the following is not a perfect cube?
- A
$216$
- B
$1000$
- ✓
$243$
- D
$1331$
Answer$243=3 \times 3 \times 3 \times 3 \times 3=3^{3} \times 3^{2}$
View full question & answer→MCQ 2291 Mark
The prime factorisation of $64$ is:
- A
$2 \times 2 \times 2$
- ✓
$4 \times 4 \times 4$
- C
$8 x 8 x 8$
- D
AnswerCorrect option: B. $4 \times 4 \times 4$
$64=4^{3}=4 \times 4 \times 4$
View full question & answer→MCQ 2301 Mark
The one’s digit of the cube of $53$ is:
Answer$53^{3}=53 \times 53 \times 53$ $3^{3}=3 \times 3 \times 3=27$ Hence, at unit place we will get $7$ . Recheck: $53^{3}=53 \times 53 \times 53=148877$
View full question & answer→