Question 11 Mark
Find the cube of the following numbers:12
AnswerCube of $12=12^3=12 \times 12 \times 12=1728$
View full question & answer→Question 21 Mark
Fill in the blanks:
$\sqrt[3]{\frac{729}{1331}}=\frac{9}{...}$
Answer$\sqrt[3]{\frac{729}{1331}}=\frac{9}{\underline{11}}$
Solution:
$\because\sqrt[3]{\frac{729}{1331}}$
$=\frac{\sqrt[3]{27}}{{\sqrt[3]{1331}}}$
$=\frac{9}{\underline{11}}$
View full question & answer→Question 31 Mark
Write true (T) or false (F) for the following statement:
No cube can end with exactly two zeros.
AnswerTrue.
Solution:
Because a perfect cube always ends with multiples of 3 zeros, e.g., 3 zeros, 6 zeros etc.
View full question & answer→Question 41 Mark
Write the units digit of the cube of the following numbers:
44447
AnswerProperties:
If a numbers ends with digits 1, 4, 5, 6 or 9, its cube will have the same ending digit.
If a number ends with 2, its cube will end with 8.
If a number ends with 8, its cube will end with 2.
If a number ends with 3, its cube will end with 7.
If a number ends with 7, its cube will end with 3.
From the above properties, we get:
Cube of the number 44447 will end with 3.
View full question & answer→Question 51 Mark
Write true (T) or false (F) for the following statement:
There is no perfect cube which ends in 4.
AnswerFalse.
Solution:
64 is a perfect cube, and it ends with 4.
View full question & answer→Question 61 Mark
AnswerWe have:
$2.1=\frac{21}{10}$
Also, $\Big(\frac{\text{m}}{\text{n}}\Big)^3=\frac{\text{m}^3}{\text{n}^3}$
$\therefore\Big(\frac{21}{10}\Big)^3$
$=\frac{21^3}{10^3}$
$=\frac{21\times21\times21}{10\times10\times10}$
$=\frac{9261}{1000}$
$=9.261$
View full question & answer→Question 71 Mark
Find the cube of:
$-12$
AnswerCube of -12 is given as:
$(-12)^3=-12 \times-12 \times-12=-1728$
Thuse, the of -12 is $(-1728)$
View full question & answer→Question 81 Mark
Evaluate:
$\sqrt[3]{4^3\times6^3}$
AnswerProperty:
For any two integers a and b, $\sqrt[3]{\text{ab}}=\sqrt[3]{\text{a}}\times\sqrt[3]{\text{b}},$
From the above property, we have:
$\sqrt[3]{-4^3\times6^3}$
$=\sqrt[3]{4^3}\times\sqrt[3]{6^3}$
$=4\times6=24$
View full question & answer→Question 91 Mark
Write the units digit of the cube of the following number:
388
AnswerProperties:
If a numbers ends with digits 1, 4, 5, 6 or 9, its cube will have the same ending digit.
If a number ends with 2, its cube will end with 8.
If a number ends with 8, its cube will end with 2.
If a number ends with 3, its cube will end with 7.
If a number ends with 7, its cube will end with 3.
From the above propertie, we get:
Cube of the number 388 will end with 2.
View full question & answer→Question 101 Mark
Find the units digit of the cube root of the following numbers:
13824
AnswerCube root using units digit:
Let us consider the number 13824.
The unit digit is 4; therefore, the unit digit of the cube root of 13824 is 4.
View full question & answer→Question 111 Mark
Write true (T) or false (F) for the following statement:
8640 is not a perfect cube.
AnswerTrue.
Solution:
On factorising 8640 into prime factors, we got:
8640 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5
On grouping the factors in triples of equal factors, we get:
8640 = {2 × 2 × 2} × {2 × 2 × 2} × {3 × 3 × 3} × 5
It is evident that the prime factors of 8640 cannot be grouped into triples of equal factors such that no factor is left over. Therefore, 8640 is not a perfect cube.
View full question & answer→Question 121 Mark
Find the cube of:
$-\frac{8}{11}$
Answer$\because\Big(\frac{\text{m}}{\text{n}}\Big)^3=\frac{\text{m}^3}{\text{n}^3}$
$\therefore\Big(-\frac{8}{11}\Big)^3= \Big(\frac{8^3}{11^3}\Big)$
$ =\Big(\frac{8\times8\times8}{11\times11\times11}\Big)=\frac{512}{131}$
View full question & answer→Question 131 Mark
Find the cube of the following numbers:
$16$
AnswerCube of $16=16^3=16 \times 16 \times 16=4096$
View full question & answer→Question 141 Mark
Find the cube of:
$3\frac{1}{4}$
AnswerWe have:
$3\frac{1}{4}=\frac{13}{4}$
$\because\Big(\frac{\text{m}}{\text{n}}\Big)^3=\frac{\text{m}^3}{\text{n}^3}$
$\therefore\Big(\frac{13}{4}\Big)^3$
$=\frac{13^3}{4^3}$
$=\frac{13\times13\times13}{4\times4\times4}$
$=\frac{2197}{64}$
View full question & answer→Question 151 Mark
Find which of the following numbers are cubes of rational numbers:
$\frac{27}{64}$
AnswerWe have:
$\frac{27}{64}$
$=\frac{3\times3\times3}{8\times8\times8}$
$=\frac{3^3}{8^3}$
$=\Big(\frac{3}{8}\Big)^3$
Therefore, $\frac{27}{64}$ is a cube of $\frac{3}{8}$.
View full question & answer→Question 161 Mark
Find the cube of the following numbers:
$302$
AnswerCube of $302=302^3=302 \times 302 \times 302=27543608$
View full question & answer→Question 171 Mark
Find the cube of the following numbers:
40
AnswerCube of $40=40^3=40 \times 40 \times 40=64000$
View full question & answer→Question 181 Mark
Find which of the following number are cubes of rational number:
$\frac{125}{128}$
AnswerWe have:
$\frac{125}{128}$
$=\frac{5\times5\times5}{2\times2\times2\times2\times2\times2\times2}$
$=\frac{5^3}{2^3\times2^3\times2}$
$=\Big(\frac{3}{8}\Big)^3$
It is evident that 128 cannot be grouped into triples of equal factors; therefore, $\frac{125}{128}$ is not a cube of a rational number.
View full question & answer→Question 191 Mark
AnswerWe have:
$1.5=\frac{15}{10}$
Also, $\Big(\frac{\text{m}}{\text{n}}\Big)^3=\frac{\text{m}^3}{\text{n}^3}$
$\therefore\Big(\frac{15}{10}\Big)^3$
$=\frac{15^3}{10^3}$
$=\frac{15\times15\times15}{10\times10\times10}$
$=\frac{3375}{1000}$
$=3.375$
View full question & answer→Question 201 Mark
Write the units digit of the cube of the following numbers:
77774
AnswerProperties:
If a numbers ends with digits 1, 4, 5, 6 or 9, its cube will have the same ending digit.
If a number ends with 2, its cube will end with 8.
If a number ends with 8, its cube will end with 2.
If a number ends with 3, its cube will end with 7.
If a number ends with 7, its cube will end with 3.
From the above properties, we get:
Cube of the number 77774 will end with 4.
View full question & answer→Question 211 Mark
Find the cube of:
$-21$
AnswerCube of -21 is given as:
$(-21)^3=-21 \times-21 \times-21=-9261$
Thuse, the of -21 is $(-9261)$
View full question & answer→Question 221 Mark
Find which of the following number are cubes of rational number:0.04
AnswerWe have:
0.04
$=\frac{4}{10}$
$=\frac{2\times2}{2\times2\times5\times5}$
It is evident that 4 and 100 could not be grouped in to triples of equal factors; therefore, 0.04 is not a cube of a rational number.
View full question & answer→Question 231 Mark
Fill in the blanks:
$\sqrt[3]{480}=\sqrt[3]{3}\times2\times\sqrt[3]{...}$
Answer$\sqrt[3]{480}=\sqrt[3]{3}\times2\times\sqrt[3]{\underline{20}}$
Solution:
$\because\sqrt[3]{480}=\sqrt[3]{\{2\times2\times2\}\times2\times2\times3\times5}$
$=2\times\sqrt[3]{3}\times\sqrt[3]{5\times2\times2}$
$=\sqrt[3]{3\times2\times\sqrt[3]{20}}$
View full question & answer→Question 241 Mark
Find the cube of the following numbers:
$55$
AnswerCube of $55=55^3=55 \times 55 \times 55=166375$
View full question & answer→Question 251 Mark
Write true ( T ) or false ( F ) for the following statement:
If $a$ and $b$ are integers such that $a^2>b^2$, then $a^3>b^3$.
AnswerFalse.
Solution:
It is not true for negative integers.
Example:
$(-5)^2 > (-4)^2$ but $(-5)^3<(-4)^3$
View full question & answer→Question 261 Mark
Write the units digit of the cube of the following number:
833
AnswerProperties:
If a numbers ends with digits 1, 4, 5, 6 or 9, its cube will have the same ending digit.
If a number ends with 2, its cube will end with 8.
If a number ends with 8, its cube will end with 2.
If a number ends with 3, its cube will end with 7.
If a number ends with 7, its cube will end with 3.
From the above propertie, we get:
Cube of the number 833 will end with 7.
View full question & answer→Question 271 Mark
Write the units digit of the cube of the following numbers:
4276
AnswerProperties:
If a numbers ends with digits 1, 4, 5, 6 or 9, its cube will have the same ending digit.
If a number ends with 2, its cube will end with 8.
If a number ends with 8, its cube will end with 2.
If a number ends with 3, its cube will end with 7.
If a number ends with 7, its cube will end with 3.
From the above properties, we get:
Cube of the number 4276 will end with 6.
View full question & answer→Question 281 Mark
Write true (T) or false (F) for the following statement:
For an integer $a, a^3$ is always greater than $a^2$.
AnswerFalse.
Solution:
It is not true for a negative integer.
Example:
$(-5)^2=25 ;(-5)^3$
$=-125$
$\Rightarrow(-5)^3<(-5)^2$
View full question & answer→Question 291 Mark
Write the units digit of the cube of the following numbers:
5922
AnswerProperties:
If a numbers ends with digits 1, 4, 5, 6 or 9, its cube will have the same ending digit.
If a number ends with 2, its cube will end with 8.
If a number ends with 8, its cube will end with 2.
If a number ends with 3, its cube will end with 7.
If a number ends with 7, its cube will end with 3.
From the above properties, we get:
Cube of the number 5922 will end with 8.
View full question & answer→Question 301 Mark
Find the cube of:
$\frac{12}{7}$
Answer$\because\Big(\frac{\text{m}}{\text{n}}\Big)^3=\frac{\text{m}^3}{\text{n}^3}$
$\therefore\Big(\frac{12}{7}\Big)^3$
$=\frac{12^3}{7^3}$
$=\frac{12\times12\times12}{7\times7\times7}$
$=\frac{1728}{343}$
View full question & answer→Question 311 Mark
Fill in the blanks:
$\sqrt[]{...}=\sqrt[3]{7} \times \sqrt[3]{8 }$
Answer$\sqrt[3]{\underline{7{\times8}}}=\sqrt[3]{7} \times \sqrt[3]{8 }$
Solution:
$\sqrt[3]{\underline{7{\times8}}}=\sqrt[3]{7} \times \sqrt[3]{8 }$
View full question & answer→Question 321 Mark
Write the units digit of the cube of the following number:
109
AnswerProperties:
If a numbers ends with digits 1, 4, 5, 6 or 9, its cube will have the same ending digit.
If a number ends with 2, its cube will end with 8.
If a number ends with 8, its cube will end with 2.
If a number ends with 3, its cube will end with 7.
If a number ends with 7, its cube will end with 3.
From the above propertie, we get:
Cube of the number 109 will end with 9.
View full question & answer→Question 331 Mark
Write true ( T ) or false ( F ) for the following statement:
If $a^2$ ends in 9 , then $a^3$ ends in 7.
AnswerFalse.
Solution:
$a^3$ ends in 7 if $a$ ends with 3.
But for every $a^2$ ending in 9 , it is not necessary that $a$ is 3 .
E.g., 49 is a square of 7 and cube of 7 is 343.
View full question & answer→Question 341 Mark
Write the units digit of the cube of the following number:
31,
AnswerProperties:
If a numbers ends with digits 1, 4, 5, 6 or 9, its cube will have the same ending digit.
If a number ends with 2, its cube will end with 8.
If a number ends with 8, its cube will end with 2.
If a number ends with 3, its cube will end with 7.
If a number ends with 7, its cube will end with 3.
From the above propertie, we get:
Cube of the number 31 will end with 1.
View full question & answer→Question 351 Mark
Find the cube root of the following rational numbers:
1.131
AnswerWe have:
$1.131=\frac{1331}{1000}$
$\therefore\sqrt[3]{1.331}$
$=\sqrt[]{\frac{1331}{1000}}$
$={\frac{\sqrt[3]{1331}}{\sqrt[3]{1000}}}$
$={\frac{\sqrt[3]{11\times11\times11}}{\sqrt[3]{1000}}}$
$=\frac{11}{10}=1.1$
View full question & answer→Question 361 Mark
Find the units digit of the cube root of the following numbers:
571787
AnswerCube root using units digit:
Let us consider the number 571787.
The unit digit is 7; therefore, the unit digit of the cube root of 571787 is 3.
View full question & answer→Question 371 Mark
AnswerWe have:
$0.08=\frac{8}{100}$
Also, $\Big(\frac{\text{m}}{\text{n}}\Big)^3=\frac{\text{m}^3}{\text{n}^3}$
$\therefore\Big(\frac{8}{100}\Big)^3$
$=\frac{8^3}{100^3}$
$=\frac{8\times8\times8}{100\times100\times100}$
$=\frac{512}{1000000}$
$=0.000512$
View full question & answer→Question 381 Mark
Find the cube root of the following rational numbers:
0.001
AnswerWe have:
$0.001=\frac{1}{1000}$
$\therefore\sqrt[3]{0.001}$
$=\sqrt[]{\frac{1}{1000}}$
$={\frac{\sqrt[3]{1}}{\sqrt[3]{1000}}}$
$\frac{1}{10}=0.1$
View full question & answer→Question 391 Mark
Write true (T) or false (F) for the following statement:
If a divides $b$, then $a^3$ divides $b^3$.
AnswerTrue.
Solution:
$\because$ a divides b
$\therefore \frac{ b ^3}{ a ^3}=\frac{ b \times b \times b }{ a \times a \times a }=\frac{( ak ) \times( ak ) \times( ak )}{ a \times a \times a }$
$\because$ a divides b
$\therefore b = ak$ fore some k
$\therefore \frac{ b ^3}{ a ^3}=\frac{( ak ) \times( ak ) \times( ak )}{ a \times a \times a }= k ^3$
$\Rightarrow k ^3= b ^3= a ^3\left( k ^3\right)$
$\therefore a^3$ divides $b^3$
View full question & answer→Question 401 Mark
Evaluate the following:
$\sqrt[3]{\frac{729}{216}}\times\frac{6}{9}$
AnswerTo evaluate the value of the given expression, we need to proceed as follows:
$\sqrt[3]{\frac{729}{216}}\times\frac{6}{9}$
${\frac{\sqrt[3]{729}}{\sqrt[3]{216}}}\times\frac{6}{9}$
$=\frac{\sqrt[3]{9\times9\times9}}{\sqrt[3]{2\times2\times2\times3\times3\times3}}\times\frac{6}{9}$
$=\frac{9}{2\times3}\times\frac{6}{9}$
$=\frac{9^1}{6}\times\frac{6^1}{9}=1$
Thus, the answer is 1.
View full question & answer→Question 411 Mark
Find the cube of the following numbers:
$100$
AnswerCube of $100=100^3=100 \times 100 \times 100=1000000$
View full question & answer→Question 421 Mark
Find the units digit of the cube root of the following numbers:
226981
AnswerCube root using units digit:
Let us consider the number 226981.
The unit digit is 1; therefore, the unit digit of the cube root of 226981 is 1.
View full question & answer→Question 431 Mark
Fill in the blanks:
$\sqrt[]{\frac{512}{...}} = \frac{8}{13}$
Answer13 × 13 × 13 = 2197
Solution:
$\because\sqrt[3]{\frac{512}{\underline{13}}}$
$=\frac{\sqrt[3]{8^3}}{{\sqrt[3]{13^3}}}$
$=\frac{8}{\underline{13}}$
View full question & answer→Question 441 Mark
Find which of the following number are cubes of rational number:
0.001331
AnswerWe have:
0.001331
=$\frac{1331}{1000000}$
$=\frac{11\times11\times11}{2\times2\times2\times2\times2\times2\times5\times5\times5\times5\times5\times5}$
$=\frac{11^3}{(2\times2\times5\times5)^3}$
$=\frac{11^3}{100^3}$
$=\Big(\frac{11}{100}\Big)$
Therefore, 0.001331 is a cube of $\frac{11}{100}$
View full question & answer→Question 451 Mark
Find the cube of:
$-\frac{13}{8}$
Answer$\because\Big(-\frac{\text{m}}{\text{n}}\Big)^3=-\frac{\text{m}^3}{\text{n}^3}$
$\therefore\Big(-\frac{13}{8}\Big)^3$
$=-\Big(\frac{13}{8}\Big)^3$
$=-\Big(\frac{13^3}{8^3}\Big)$
$=-\Big(\frac{13\times13\times13}{8\times8\times8}\Big)$
$=-\frac{2197}{512}$
View full question & answer→Question 461 Mark
Find the cube of the following numbers:
$301$
AnswerCube of $100=100^3=100 \times 100 \times 100=1000000$
View full question & answer→Question 471 Mark
Evaluate:
$\sqrt[3]{8\times17\times17\times17}$
AnswerProperty:
For any two integers a and b, $\sqrt[3]{\text{ab}}=\sqrt[3]{\text{a}}\times\sqrt[3]{\text{b}},$
From the above property, we have:
$\sqrt[3]{8\times17\times17\times17}$
$=\sqrt[3]{2^3\times17^3}$
$=\sqrt[3]{2^3}\times\sqrt[3]{17^3}$
$=2\times17=34$
View full question & answer→Question 481 Mark
Write true ( $T$ ) or false ( $F$ ) for the following statement:
If $a^2$ ends in an even number of zeros, then $a^3$ ends in an odd number of zeros.
AnswerFalse.
$\because 100^2=10000 \text { but } 100^3=100000$
View full question & answer→Question 491 Mark
Write the units digit of the cube of the following numbers:
125125125
AnswerProperties:
If a numbers ends with digits 1, 4, 5, 6 or 9, its cube will have the same ending digit.
If a number ends with 2, its cube will end with 8.
If a number ends with 8, its cube will end with 2.
If a number ends with 3, its cube will end with 7.
If a number ends with 7, its cube will end with 3.
From the above properties, we get:
Cube of the number 125125125 will end with 5.
View full question & answer→Question 501 Mark
Fill in the blanks:
$\sqrt[3]{8\times...}=8$
Answer$8\times8=64$
Solution:
$\because\sqrt[3]{8\times\underline{8\times8}}=8$
View full question & answer→Question 511 Mark
Find the cube of the following numbers:
$21$
AnswerCube of $21=21^3=21 \times 21 \times 21=9261$
View full question & answer→Question 521 Mark
Find the cube of:
$-11$
AnswerCube of -11 is given as:
$(-11)^3=-11 \times-11 \times-11=-1331$
Thuse, the of 11 is ( -1331 )
View full question & answer→Question 531 Mark
Find the cube of the following numbers:
7
AnswerCube of $7=7^3=7 \times 7 \times 7=343$
View full question & answer→Question 541 Mark
Write true (T) or false (F) for the following statement:
If $a^2$ ends in 5 , then $a^3$ ends in 25.
AnswerFalse.
Solution:
$\because 35^2=1225 \text { but } 53^3=42875$
View full question & answer→Question 551 Mark
Fill in the blanks:
$\sqrt[3]{\frac{27}{125}}=\frac{...}{5}$
Answer$\sqrt[3]{\frac{27}{125}}=\frac{\underline{3}}{5}$
Solution:
$\because\sqrt[3]{\frac{27}{125}}$
$=\sqrt[3]{\frac{27}{125}}$
$=\frac{\underline{3}}{5}$
View full question & answer→Question 561 Mark
AnswerWe have:
$0.3=\frac{3}{10}$
Also, $\Big(\frac{\text{m}}{\text{n}}\Big)^3=\frac{\text{m}^3}{\text{n}^3}$
$\therefore\Big(\frac{3}{10}\Big)^3$
$=\frac{3^3}{10^3}$
$=\frac{3\times3\times3}{10\times10\times10}$
$-0.027$
View full question & answer→Question 571 Mark
Find the cube root of the following numbers:
8 × 125
AnswerProperty:
For any two integers a and b, $\sqrt[3]{\text{ab}}=\sqrt[3]{\text{a}}\times\sqrt[3]{\text{b}}$
From the above property, we have:
$\sqrt[3]{8\times125}$
$=\sqrt[3]{8}\times\sqrt[3]{125}$
$=\sqrt[3]{2\times2\times2}\times\sqrt[3]{5\times5\times5}$
$=2\times5=10$
View full question & answer→Question 581 Mark
Fill in the blanks:
$\sqrt[3]{1728}=4\times...$
Answer$\sqrt[3]{1728}=4\times\underline3$
Solution:
$\because\sqrt[3]{1728}=12$
$=4\times\underline3$
View full question & answer→Question 591 Mark
Find the cube of:
$\frac{7}{9}$
Answer$\because\Big(\frac{\text{m}}{\text{n}}\Big)^3=\frac{\text{m}^3}{\text{n}^3}$
$\therefore\Big(\frac{7}{9}\Big)^3 = \frac{7^3}{9^3} =\frac{7\times7\times7}{9\times9\times9}=\frac{343}{729}$
View full question & answer→Question 601 Mark
Find the cube of:
$2\frac{2}{5}$
AnswerWe have:
$2\frac{2}{5}=\frac{12}{5}$
Also, $\because\Big(\frac{\text{m}}{\text{n}}\Big)^3=\frac{\text{m}^3}{\text{n}^3}$
$\therefore\Big(\frac{12}{5}\Big)^3$
$=\Big(\frac{12^3}{5^3}\Big)$
$=\frac{12\times12\times12}{5\times5\times5}$
$=\frac{1728}{125}$
View full question & answer→Question 611 Mark
Write true (T) or false (F) for the following statement:
392 is a perfect cube.
AnswerFalse.
Solution:
On factorising 392 into prime factors, we got:
392 = 2 × 2 × 2 × 7 × 7
On grouping the factors in triples of equal factors, we get:
392 = {2 × 2 × 2} × 7 × 7
It is evident that the prime factors of 392 cannot be grouped into triples of equal factors such that no factor is left over. Therefore, 392 is not a perfect cube.
View full question & answer→Question 621 Mark
Fill in the blanks:
$\sqrt[3]{...}={\sqrt[3]{4}}\times{\sqrt[3]{5}}\times\sqrt[3]{6}$
Answer$\sqrt[3]{\underline{4\times5\times6}}=120$
Solution:
$\because\sqrt[3]{4\times5\times6}={\sqrt[3]{4}}\times{\sqrt[3]{5}}\times\sqrt[3]{6}$
View full question & answer→Question 631 Mark
Find the cube roots of the following integers:
-125
AnswerWe have,
$=\sqrt[3]{-125}$
$=-\sqrt[3]{125}$
$=\sqrt[3]{5\times5\times5}$
$=-5$
View full question & answer→Question 641 Mark
Find the units digit of the cube root of the following numbers:
175616
AnswerCube root using units digit:
Let us consider the number 175616.
The unit digit is 6; therefore, the unit digit of the cube root of 175616 is 6.
View full question & answer→