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→