Question 11 Mark
Find the cube of the following numbers:$12$
Answer
View full question & answer→Cube of $12=12^3=12 \times 12 \times 12=1728$
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Question 21 Mark
Fill in the blanks: $\sqrt[3]{\frac{729}{1331}}=\frac{9}{...}$
Answer
View full question & answer→$\sqrt[3]{\frac{729}{1331}}=\frac{9}{\underline{11}}$ Solution: $\because\sqrt[3]{\frac{729}{1331}}$ $=\frac{\sqrt[3]{27}}{{\sqrt[3]{1331}}}$ $=\frac{9}{\underline{11}}$
Question 31 Mark
Write true $(T)$ or false $(F)$ for the following statement: No cube can end with exactly two zeros.
Answer
View full question & answer→Because a perfect cube always ends with multiples of $3$ zeros, e.g., $3$ zeros, $6$ zeros etc.
Question 41 Mark
Write the units digit of the cube of the following numbers: $44447$
Answer
View full question & answer→Properties: 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 $3.$
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 $3.$
Question 51 Mark
Write true $(T)$ or false $(F)$ for the following statement: There is no perfect cube which ends in $4.$
Answer
View full question & answer→$64$ is a perfect cube, and it ends with $4.$
Question 61 Mark
Find the cube of: $2.1$
Answer
View full question & answer→We have: $2.1=\frac{21}{10}$ Also, $\Big(\frac{\text{m}}{\text{n}}\Big)^3=\frac{\text{m}^3}{\text{n}^3}$ $\therefore\Big(\frac{21}{10}\Big)^3$ $=\frac{21^3}{10^3}$ $=\frac{21\times21\times21}{10\times10\times10}$ $=\frac{9261}{1000}$ $=9.261$
Question 71 Mark
Find the cube of:
$-12$
$-12$
Answer
View full question & answer→Cube of $-12$ is given as:
$(-12)^3=-12 \times-12 \times-12=-1728$
Thuse, the of $-12$ is $(-1728)$
$(-12)^3=-12 \times-12 \times-12=-1728$
Thuse, the of $-12$ is $(-1728)$
Question 81 Mark
Evaluate:
$\sqrt[3]{4^3\times6^3}$
$\sqrt[3]{4^3\times6^3}$
Answer
View full question & answer→ Property:
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:
$\sqrt[3]{-4^3\times6^3}$
$=\sqrt[3]{4^3}\times\sqrt[3]{6^3}$
$=4\times6=24$
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:
$\sqrt[3]{-4^3\times6^3}$
$=\sqrt[3]{4^3}\times\sqrt[3]{6^3}$
$=4\times6=24$
Question 91 Mark
Write the units digit of the cube of the following number: $388$
Answer
View full question & answer→Properties: 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 $2.$
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 $2.$
Question 101 Mark
Find the units digit of the cube root of the following numbers: $13824$
Answer
View full question & answer→Cube 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 $4.$
Question 111 Mark
Write true $(T)$ or false $(F)$ for the following statement:
$8640$ is not a perfect cube.
$8640$ is not a perfect cube.
Answer
View full question & answer→On factorising 8640 into prime factors, we got:
$8640 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 5$
On grouping the factors in triples of equal factors, we get:
$8640 = \{2 \times 2 \times 2\} \times \{2 \times 2 \times 2\} \times \{3 \times 3 \times 3\} \times 5$
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.
$8640 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 5$
On grouping the factors in triples of equal factors, we get:
$8640 = \{2 \times 2 \times 2\} \times \{2 \times 2 \times 2\} \times \{3 \times 3 \times 3\} \times 5$
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.
Question 121 Mark
Find the cube of:
$-\frac{8}{11}$
$-\frac{8}{11}$
Answer
View full question & 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}$
$\therefore\Big(-\frac{8}{11}\Big)^3= \Big(\frac{8^3}{11^3}\Big)$
$ =\Big(\frac{8\times8\times8}{11\times11\times11}\Big)=\frac{512}{131}$
Question 131 Mark
Find the cube of the following numbers:$16$
Answer
View full question & answer→Cube of $16=16^3=16 \times 16 \times 16=4096$
Question 141 Mark
Find the cube of: $3\frac{1}{4}$
Answer
View full question & answer→We have: $3\frac{1}{4}=\frac{13}{4}$ $\because\Big(\frac{\text{m}}{\text{n}}\Big)^3=\frac{\text{m}^3}{\text{n}^3}$ $\therefore\Big(\frac{13}{4}\Big)^3$ $=\frac{13^3}{4^3}$ $=\frac{13\times13\times13}{4\times4\times4}$ $=\frac{2197}{64}$
Question 151 Mark
Find which of the following numbers are cubes of rational numbers: $\frac{27}{64}$
Answer
View full question & answer→We 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 $\frac{3}{8}$.
Question 161 Mark
Find the cube of the following numbers: $302$
Answer
View full question & answer→Cube of $302=302^3=302 \times 302 \times 302=27543608$
Question 171 Mark
Find the cube of the following numbers: $40$
Answer
View full question & answer→Cube of $40=40^3=40 \times 40 \times 40=64000$
Question 181 Mark
Find which of the following number are cubes of rational number: $\frac{125}{128}$
Answer
View full question & answer→We 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.
Question 191 Mark
Find the cube of: $1.5$
Answer
View full question & answer→We have: $1.5=\frac{15}{10}$ Also, $\Big(\frac{\text{m}}{\text{n}}\Big)^3=\frac{\text{m}^3}{\text{n}^3}$ $\therefore\Big(\frac{15}{10}\Big)^3$ $=\frac{15^3}{10^3}$ $=\frac{15\times15\times15}{10\times10\times10}$ $=\frac{3375}{1000}$ $=3.375$
Question 201 Mark
Write the units digit of the cube of the following numbers: $77774$
Answer
View full question & answer→Properties: 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 $4.$
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 $4.$
Question 211 Mark
Find the cube of:
$-21$
$-21$
Answer
View full question & answer→Cube of $-21$ is given as:
$(-21)^3=-21 \times-21 \times-21=-9261$
Thuse, the of $-21$ is $(-9261)$
$(-21)^3=-21 \times-21 \times-21=-9261$
Thuse, the of $-21$ is $(-9261)$
Question 221 Mark
Find which of the following number are cubes of rational number: $0.04$
Answer
View full question & answer→We 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.
Question 231 Mark
Fill in the blanks: $\sqrt[3]{480}=\sqrt[3]{3}\times2\times\sqrt[3]{...}$
Answer
View full question & answer→$\sqrt[3]{480}=\sqrt[3]{3}\times2\times\sqrt[3]{\underline{20}}$ Solution: $\because\sqrt[3]{480}=\sqrt[3]{\{2\times2\times2\}\times2\times2\times3\times5}$ $=2\times\sqrt[3]{3}\times\sqrt[3]{5\times2\times2}$ $=\sqrt[3]{3\times2\times\sqrt[3]{20}}$
Question 241 Mark
Find the cube of the following numbers:
$55$
$55$
Answer
View full question & answer→Cube of $55=55^3=55 \times 55 \times 55=166375$
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 $a^3>b^3$.
If $a$ and $b$ are integers such that $a^2>b^2$, then $a^3>b^3$.
Answer
View full question & answer→It is not true for negative integers.
Example:
$(-5)^2 > (-4)^2$ but $(-5)^3<(-4)^3$
Example:
$(-5)^2 > (-4)^2$ but $(-5)^3<(-4)^3$
Question 261 Mark
Write the units digit of the cube of the following number: $833$
Answer
View full question & answer→Properties: 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 $7.$
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 $7.$
Question 271 Mark
Write the units digit of the cube of the following numbers: $4276$
Answer
View full question & answer→Properties: 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 $6.$
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 $6.$
Question 281 Mark
Write true $(T)$ or false $(F)$ for the following statement:
For an integer $a$, $a^3$ is always greater than $a^2$.
For an integer $a$, $a^3$ is always greater than $a^2$.
Answer
View full question & answer→It is not true for a negative integer.
Example:
$(-5)^2 = 25;(-5)^3$
$= -125$
$\Rightarrow(-5)^3<(-5)^2$
Example:
$(-5)^2 = 25;(-5)^3$
$= -125$
$\Rightarrow(-5)^3<(-5)^2$
Question 291 Mark
Write the units digit of the cube of the following numbers: $5922$
Answer
View full question & answer→Properties: 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 $8.$
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 $8.$
Question 301 Mark
Find the cube of: $\frac{12}{7}$
Answer
View full question & answer→$\because\Big(\frac{\text{m}}{\text{n}}\Big)^3=\frac{\text{m}^3}{\text{n}^3}$ $\therefore\Big(\frac{12}{7}\Big)^3$ $=\frac{12^3}{7^3}$ $=\frac{12\times12\times12}{7\times7\times7}$ $=\frac{1728}{343}$
Question 311 Mark
Fill in the blanks: $\sqrt[]{...}=\sqrt[3]{7} \times \sqrt[3]{8 }$
Answer
View full question & answer→$\sqrt[3]{\underline{7{\times8}}}=\sqrt[3]{7} \times \sqrt[3]{8 }$ Solution: $\sqrt[3]{\underline{7{\times8}}}=\sqrt[3]{7} \times \sqrt[3]{8 }$
Question 321 Mark
Write the units digit of the cube of the following number: $109$
Answer
View full question & answer→Properties: 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 $9.$
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 $9.$
Question 331 Mark
Write true $(T)$ or false $(F)$ for the following statement:
If $a^2$ ends in $9,$ then $a^3$ ends in $7.$
If $a^2$ ends in $9,$ then $a^3$ ends in $7.$
Answer
View full question & answer→$a^3$ ends in $7$ if a ends with $3.$ But for every $a2$ ending in $9,$ it is not necessary that a is $3.$ $E.g., 49$ is a square of $7$ and cube of $7$ is $343.$
Question 341 Mark
Write the units digit of the cube of the following number: $31$,
Answer
View full question & answer→Properties: 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 $1.$
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 $1.$
Question 351 Mark
Find the cube root of the following rational numbers: $ 1.131$
Answer
View full question & answer→We have: $1.131=\frac{1331}{1000}$ $\therefore\sqrt[3]{1.331}$ $=\sqrt[]{\frac{1331}{1000}}$ $={\frac{\sqrt[3]{1331}}{\sqrt[3]{1000}}}$ $={\frac{\sqrt[3]{11\times11\times11}}{\sqrt[3]{1000}}}$ $=\frac{11}{10}=1.1$
Question 361 Mark
Find the units digit of the cube root of the following numbers: $571787$
Answer
View full question & answer→Cube 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 $3.$
Question 371 Mark
Find the cube of: $0.08$
Answer
View full question & answer→We have: $0.08=\frac{8}{100}$ Also, $\Big(\frac{\text{m}}{\text{n}}\Big)^3=\frac{\text{m}^3}{\text{n}^3}$ $\therefore\Big(\frac{8}{100}\Big)^3$ $=\frac{8^3}{100^3}$ $=\frac{8\times8\times8}{100\times100\times100}$ $=\frac{512}{1000000}$ $=0.000512$
Question 381 Mark
Find the cube root of the following rational numbers: $0.001$
Answer
View full question & answer→We have: $0.001=\frac{1}{1000}$
$\therefore\sqrt[3]{0.001}$
$=\sqrt[]{\frac{1}{1000}}$
$={\frac{\sqrt[3]{1}}{\sqrt[3]{1000}}}$
$\frac{1}{10}=0.1$
$\therefore\sqrt[3]{0.001}$
$=\sqrt[]{\frac{1}{1000}}$
$={\frac{\sqrt[3]{1}}{\sqrt[3]{1000}}}$
$\frac{1}{10}=0.1$
Question 391 Mark
Write true $(T)$ or false $(F)$ for the following statement:
If $a$ divides $b$, then $a^3$ divides $b^3$.
If $a$ divides $b$, then $a^3$ divides $b^3$.
Answer
View full question & answer→$\because a$ divides $b$
$\therefore\frac{\text{b}^3}{\text{a}^3}=\frac{\text{b}\times\text{b}\times\text{b}}{\text{a}\times\text{a}\times\text{a}}=\frac{\text{(ak)}\times\text{(ak)}\times\text{(ak)}}4{\text{a}\times\text{a}\times\text{a}}$
$\because$ a divides b
$\therefore b = ak$ fore some $k$
$\therefore\frac{\text{b}^3}{\text{a}^3}=\frac{\text{(ak)}\times\text{(ak)}\times\text{(ak)}}{\text{a}\times\text{a}\times\text{a}}
=\text{k}^3$ $\Rightarrow\text{k}^3=\text{b}^3=\text{a}^3(\text{k}^3)$
$\therefore$ $a^3$ divides $b^3$
$\therefore\frac{\text{b}^3}{\text{a}^3}=\frac{\text{b}\times\text{b}\times\text{b}}{\text{a}\times\text{a}\times\text{a}}=\frac{\text{(ak)}\times\text{(ak)}\times\text{(ak)}}4{\text{a}\times\text{a}\times\text{a}}$
$\because$ a divides b
$\therefore b = ak$ fore some $k$
$\therefore\frac{\text{b}^3}{\text{a}^3}=\frac{\text{(ak)}\times\text{(ak)}\times\text{(ak)}}{\text{a}\times\text{a}\times\text{a}}
=\text{k}^3$ $\Rightarrow\text{k}^3=\text{b}^3=\text{a}^3(\text{k}^3)$
$\therefore$ $a^3$ divides $b^3$
Question 401 Mark
Evaluate the following: $\sqrt[3]{\frac{729}{216}}\times\frac{6}{9}$
Answer
View full question & answer→To 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 $1.$
$\sqrt[3]{\frac{729}{216}}\times\frac{6}{9}$
${\frac{\sqrt[3]{729}}{\sqrt[3]{216}}}\times\frac{6}{9}$
$=\frac{\sqrt[3]{9\times9\times9}}{\sqrt[3]{2\times2\times2\times3\times3\times3}}\times\frac{6}{9}$
$=\frac{9}{2\times3}\times\frac{6}{9}$
$=\frac{9^1}{6}\times\frac{6^1}{9}=1$ Thus, the answer is $1.$
Question 411 Mark
Find the cube of the following numbers:
$100$
$100$
Answer
View full question & answer→Cube of $100=100^3=100 \times 100 \times 100=1000000$
Question 421 Mark
Find the units digit of the cube root of the following numbers: $226981$
Answer
View full question & answer→Cube 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 $1.$
Question 431 Mark
Fill in the blanks: $\sqrt[]{\frac{512}{...}} = \frac{8}{13}$
Answer
View full question & answer→$13 \times 13 \times 13 = 2197$
Solution:
$\because\sqrt[3]{\frac{512}{\underline{13}}}$
$=\frac{\sqrt[3]{8^3}}{{\sqrt[3]{13^3}}}$
$=\frac{8}{\underline{13}}$
Solution:
$\because\sqrt[3]{\frac{512}{\underline{13}}}$
$=\frac{\sqrt[3]{8^3}}{{\sqrt[3]{13^3}}}$
$=\frac{8}{\underline{13}}$
Question 441 Mark
Find which of the following number are cubes of rational number: $0.001331$
Answer
View full question & answer→We 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 $\frac{11}{100}$
$=\frac{11\times11\times11}{2\times2\times2\times2\times2\times2\times5\times5\times5\times5\times5\times5}$
$=\frac{11^3}{(2\times2\times5\times5)^3}$
$=\frac{11^3}{100^3}$
$=\Big(\frac{11}{100}\Big)$
Therefore, $0.001331$ is a cube of $\frac{11}{100}$
Question 451 Mark
Find the cube of: $-\frac{13}{8}$
Answer
View full question & answer→$\because\Big(-\frac{\text{m}}{\text{n}}\Big)^3=-\frac{\text{m}^3}{\text{n}^3}$ $\therefore\Big(-\frac{13}{8}\Big)^3$ $=-\Big(\frac{13}{8}\Big)^3$ $=-\Big(\frac{13^3}{8^3}\Big)$ $=-\Big(\frac{13\times13\times13}{8\times8\times8}\Big)$ $=-\frac{2197}{512}$
Question 461 Mark
Find the cube of the following numbers:
$301$
$301$
Answer
View full question & answer→Cube of $301=301^3=301 \times 301 \times 30=27270901$
Question 471 Mark
Evaluate: $\sqrt[3]{8\times17\times17\times17}$
Answer
View full question & answer→Property: 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: $\sqrt[3]{8\times17\times17\times17}$ $=\sqrt[3]{2^3\times17^3}$ $=\sqrt[3]{2^3}\times\sqrt[3]{17^3}$ $=2\times17=34$
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.
If $a^2$ ends in an even number of zeros, then $a^3$ ends in an odd number of zeros.
Answer
View full question & answer→False.
Solution:
$\because$ $100^2=10000$ but $100^5=100000$
Solution:
$\because$ $100^2=10000$ but $100^5=100000$
Question 491 Mark
Write the units digit of the cube of the following numbers: $125125125$
Answer
View full question & answer→Properties: 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 $5.$
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 $5.$
Question 501 Mark
Fill in the blanks: $\sqrt[3]{8\times...}=8$
Answer
View full question & answer→$8\times8=64$ Solution: $\because\sqrt[3]{8\times\underline{8\times8}}=8$
Question 511 Mark
Find the cube of the following numbers:
$21$
$21$
Answer
View full question & answer→Cube of $21=21^3=21 \times 21 \times 21=9261$
Question 521 Mark
Find the cube of:
$-11$
$-11$
Answer
View full question & answer→Cube of $-11$ is given as:
$(-11)^3=-11 \times-11 \times-11=-1331$
Thuse, the of $11$ is $(-1331)$
$(-11)^3=-11 \times-11 \times-11=-1331$
Thuse, the of $11$ is $(-1331)$
Question 531 Mark
Find the cube of the following numbers:
$7$
$7$
Answer
View full question & answer→Cube of $7 = 7^3 = 7 × 7 × 7 = 343$
Question 541 Mark
Write true $(T)$ or false $(F)$ for the following statement:
If $a ^2$ ends in $5 ,$ then $a ^3$ ends in $25 .$
If $a ^2$ ends in $5 ,$ then $a ^3$ ends in $25 .$
Answer
View full question & answer→ $\because$ $35^2= 1225$ but $53^3 = 42875$
Question 551 Mark
Fill in the blanks: $\sqrt[3]{\frac{27}{125}}=\frac{...}{5}$
Answer
View full question & answer→$\sqrt[3]{\frac{27}{125}}=\frac{\underline{3}}{5}$ Solution: $\because\sqrt[3]{\frac{27}{125}}$ $=\sqrt[3]{\frac{27}{125}}$ $=\frac{\underline{3}}{5}$
Question 561 Mark
Find the cube of: $0.3$
Answer
View full question & answer→We have: $0.3=\frac{3}{10}$
Also, $\Big(\frac{\text{m}}{\text{n}}\Big)^3=\frac{\text{m}^3}{\text{n}^3}$
$\therefore\Big(\frac{3}{10}\Big)^3$
$=\frac{3^3}{10^3}$
$=\frac{3\times3\times3}{10\times10\times10}$
$-0.027$
Also, $\Big(\frac{\text{m}}{\text{n}}\Big)^3=\frac{\text{m}^3}{\text{n}^3}$
$\therefore\Big(\frac{3}{10}\Big)^3$
$=\frac{3^3}{10^3}$
$=\frac{3\times3\times3}{10\times10\times10}$
$-0.027$
Question 571 Mark
Find the cube root of the following numbers: $8 × 125$
Answer
View full question & answer→Property: 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: $\sqrt[3]{8\times125}$
$=\sqrt[3]{8}\times\sqrt[3]{125}$
$=\sqrt[3]{2\times2\times2}\times\sqrt[3]{5\times5\times5}$
$=2\times5=10$
$\sqrt[3]{\text{ab}}=\sqrt[3]{\text{a}}\times\sqrt[3]{\text{b}}$
From the above property,
we have: $\sqrt[3]{8\times125}$
$=\sqrt[3]{8}\times\sqrt[3]{125}$
$=\sqrt[3]{2\times2\times2}\times\sqrt[3]{5\times5\times5}$
$=2\times5=10$
Question 581 Mark
Fill in the blanks: $\sqrt[3]{1728}=4\times...$
Answer
View full question & answer→$\sqrt[3]{1728}=4\times\underline3$ Solution: $\because\sqrt[3]{1728}=12$ $=4\times\underline3$
Question 591 Mark
Find the cube of: $\frac{7}{9}$
Answer
View full question & answer→$\because\Big(\frac{\text{m}}{\text{n}}\Big)^3=\frac{\text{m}^3}{\text{n}^3}$ $\therefore\Big(\frac{7}{9}\Big)^3 = \frac{7^3}{9^3} =\frac{7\times7\times7}{9\times9\times9}=\frac{343}{729}$
Question 601 Mark
Find the cube of: $2\frac{2}{5}$
Answer
View full question & answer→We have: $2\frac{2}{5}=\frac{12}{5}$ Also, $\because\Big(\frac{\text{m}}{\text{n}}\Big)^3=\frac{\text{m}^3}{\text{n}^3}$ $\therefore\Big(\frac{12}{5}\Big)^3$ $=\Big(\frac{12^3}{5^3}\Big)$ $=\frac{12\times12\times12}{5\times5\times5}$ $=\frac{1728}{125}$
Question 611 Mark
Write true $(T)$ or false $(F)$ for the following statement: $392$ is a perfect cube.
Answer
View full question & answer→On factorising 392 into prime factors,
we got: $392 = 2 \times 2 \times 2 \times 7 \times 7$ On grouping the factors in triples of equal factors,
we get: $392 = \{2 \times 2 \times 2\} \times 7 \times 7$ 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.
we got: $392 = 2 \times 2 \times 2 \times 7 \times 7$ On grouping the factors in triples of equal factors,
we get: $392 = \{2 \times 2 \times 2\} \times 7 \times 7$ 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.
Question 621 Mark
Fill in the blanks: $\sqrt[3]{...}={\sqrt[3]{4}}\times{\sqrt[3]{5}}\times\sqrt[3]{6}$
Answer
View full question & answer→$\sqrt[3]{\underline{4\times5\times6}}=120$ Solution: $\because\sqrt[3]{4\times5\times6}={\sqrt[3]{4}}\times{\sqrt[3]{5}}\times\sqrt[3]{6}$
Question 631 Mark
Find the cube roots of the following integers: $-125$
Answer
View full question & answer→We have, $=\sqrt[3]{-125}$
$=-\sqrt[3]{125}$
$=\sqrt[3]{5\times5\times5}$
$=-5$
$=-\sqrt[3]{125}$
$=\sqrt[3]{5\times5\times5}$
$=-5$
Question 641 Mark
Find the units digit of the cube root of the following numbers: $175616$
Answer
View full question & answer→Cube 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 $6.$
Question 651 Mark
Answer
View full question & answer→Properties:
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.
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.
Question 661 Mark
Write the units digit of the cube of the following numbers:
5922
5922
Answer
View full question & answer→Properties:
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.
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.
Question 671 Mark
Write the units digit of the cube of the following numbers:
44447
44447
Answer
View full question & answer→Properties:
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.
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.
Question 681 Mark
Write the units digit of the cube of the following numbers:
4276
4276
Answer
View full question & answer→Properties:
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.
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.
Question 691 Mark
Write the units digit of the cube of the following numbers:
125125125
125125125
Answer
View full question & answer→Properties:
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.
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.
Question 701 Mark
Write the units digit of the cube of the following number:
833
833
Answer
View full question & answer→Properties:
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.
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.
Question 711 Mark
Write the units digit of the cube of the following number:
388
388
Answer
View full question & answer→Properties:
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.
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.
Question 721 Mark
Write the units digit of the cube of the following number:
31
31
Answer
View full question & answer→Properties: 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.
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.
Question 731 Mark
Write the units digit of the cube of the following number:
109
109
Answer
View full question & answer→Properties:
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.
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.
Question 741 Mark
Find which of the following numbers are cubes of rational numbers:
$\frac{27}{64}$
$\frac{27}{64}$
Answer
View full question & answer→We 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 $\frac{3}{8}$.
$\frac{27}{64}$
$=\frac{3\times3\times3}{8\times8\times8}$
$=\frac{3^3}{8^3}$
$=\Big(\frac{3}{8}\Big)^3$
Therefore, $\frac{27}{64}$ is a cube of $\frac{3}{8}$.
Question 751 Mark
Find which of the following number are cubes of rational number:
$\frac{125}{128}$
$\frac{125}{128}$
Answer
View full question & answer→We 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.
$\frac{125}{128}$
$=\frac{5\times5\times5}{2\times2\times2\times2\times2\times2\times2}$
$=\frac{5^3}{2^3\times2^3\times2}$
$=\Big(\frac{3}{8}\Big)^3$
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.
Question 761 Mark
Find which of the following number are cubes of rational number:
0.04
0.04
Answer
View full question & answer→We 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.
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.
Question 771 Mark
Find which of the following number are cubes of rational number:
0.001331
0.001331
Answer
View full question & answer→We 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 $\frac{11}{100}$
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 $\frac{11}{100}$
Question 781 Mark
Find the units digit of the cube root of the following numbers:
571787
571787
Answer
View full question & answer→Cube 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.
Let us consider the number 571787.
The unit digit is 7; therefore, the unit digit of the cube root of 571787 is 3.
Question 791 Mark
Find the units digit of the cube root of the following numbers:
226981
226981
Answer
View full question & answer→Cube 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.
Let us consider the number 226981.
The unit digit is 1; therefore, the unit digit of the cube root of 226981 is 1.
Question 801 Mark
Find the units digit of the cube root of the following numbers:
175616
175616
Answer
View full question & answer→Cube 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.
Let us consider the number 175616.
The unit digit is 6; therefore, the unit digit of the cube root of 175616 is 6.
Question 811 Mark
Find the units digit of the cube root of the following numbers:
13824
13824
Answer
View full question & answer→Cube 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.
Let us consider the number 13824.
The unit digit is 4; therefore, the unit digit of the cube root of 13824 is 4.
Question 821 Mark
Find the cube of the following numbers:
40
40
Answer
View full question & answer→Cube of 40 = 403 = 40 × 40 × 40 = 64000
Question 831 Mark
Find the cube roots of the following integers:
-125
-125
Answer
View full question & answer→We have,
$=\sqrt[3]{-125}$
$=-\sqrt[3]{125}$
$=\sqrt[3]{5\times5\times5}$
$=-5$
$=\sqrt[3]{-125}$
$=-\sqrt[3]{125}$
$=\sqrt[3]{5\times5\times5}$
$=-5$
Question 841 Mark
Find the cube root of the following rational numbers:
1.131
1.131
Answer
View full question & answer→We have:
$1.131=\frac{1331}{1000}$
$\therefore\sqrt[3]{1.331}$
$=\sqrt[]{\frac{1331}{1000}}$
$={\frac{\sqrt[3]{1331}}{\sqrt[3]{1000}}}$
$={\frac{\sqrt[3]{11\times11\times11}}{\sqrt[3]{1000}}}$
$=\frac{11}{10}=1.1$
$1.131=\frac{1331}{1000}$
$\therefore\sqrt[3]{1.331}$
$=\sqrt[]{\frac{1331}{1000}}$
$={\frac{\sqrt[3]{1331}}{\sqrt[3]{1000}}}$
$={\frac{\sqrt[3]{11\times11\times11}}{\sqrt[3]{1000}}}$
$=\frac{11}{10}=1.1$
Question 851 Mark
Find the cube root of the following rational numbers:
0.001
0.001
Answer
View full question & answer→We have:
$0.001=\frac{1}{1000}$
$\therefore\sqrt[3]{0.001}$
$=\sqrt[]{\frac{1}{1000}}$
$={\frac{\sqrt[3]{1}}{\sqrt[3]{1000}}}$
$\frac{1}{10}=0.1$
$0.001=\frac{1}{1000}$
$\therefore\sqrt[3]{0.001}$
$=\sqrt[]{\frac{1}{1000}}$
$={\frac{\sqrt[3]{1}}{\sqrt[3]{1000}}}$
$\frac{1}{10}=0.1$
Question 861 Mark
Find the cube root of the following numbers:
8 × 125
8 × 125
Answer
View full question & answer→Property:
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:
$\sqrt[3]{8\times125}$
$=\sqrt[3]{8}\times\sqrt[3]{125}$
$=\sqrt[3]{2\times2\times2}\times\sqrt[3]{5\times5\times5}$
$=2\times5=10$
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:
$\sqrt[3]{8\times125}$
$=\sqrt[3]{8}\times\sqrt[3]{125}$
$=\sqrt[3]{2\times2\times2}\times\sqrt[3]{5\times5\times5}$
$=2\times5=10$
Question 871 Mark
Find the cube of the following numbers:
7
7
Answer
View full question & answer→Cube of 7 = 73 = 7 × 7 × 7 = 343
Question 881 Mark
Find the cube of the following numbers:
55
55
Answer
View full question & answer→Cube of 55 = 553 = 55 × 55 × 55 = 166375
Question 891 Mark
Find the cube of the following numbers:
302
302
Answer
View full question & answer→Cube of 302 = 3023 = 302 × 302 × 302 = 27543608
Question 901 Mark
Find the cube of the following numbers:
301
301
Answer
View full question & answer→Cube of 301 = 3013 = 301 × 301 × 30 = 27270901
Question 911 Mark
Find the cube of the following numbers:
21
21
Answer
View full question & answer→Cube of 21 = 213 = 21 × 21 × 21 = 9261
Question 921 Mark
Find the cube of the following numbers:
16
16
Answer
View full question & answer→Cube of 16 = 163 = 16 × 16 × 16 = 4096
Question 931 Mark
Find the cube of the following numbers:
12
12
Answer
View full question & answer→Cube of 12 = 123 = 12 × 12 × 12 = 1728
Question 941 Mark
Find the cube of the following numbers:
100
100
Answer
View full question & answer→Cube of 100 = 1003 = 100 × 100 × 100 = 1000000
Question 951 Mark
Find the cube of:
$-\frac{8}{11}$
$-\frac{8}{11}$
Answer
View full question & 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}$![]()
$\therefore\Big(-\frac{8}{11}\Big)^3= \Big(\frac{8^3}{11^3}\Big)$
$ =\Big(\frac{8\times8\times8}{11\times11\times11}\Big)=\frac{512}{131}$
Question 961 Mark
Find the cube of:
$\frac{7}{9}$
$\frac{7}{9}$
Answer
View full question & answer→$\because\Big(\frac{\text{m}}{\text{n}}\Big)^3=\frac{\text{m}^3}{\text{n}^3}$
$\therefore\Big(\frac{7}{9}\Big)^3 = \frac{7^3}{9^3} =\frac{7\times7\times7}{9\times9\times9}=\frac{343}{729}$
$\therefore\Big(\frac{7}{9}\Big)^3 = \frac{7^3}{9^3} =\frac{7\times7\times7}{9\times9\times9}=\frac{343}{729}$
Question 971 Mark
Find the cube of:
$-\frac{13}{8}$
$-\frac{13}{8}$
Answer
View full question & answer→$\because\Big(-\frac{\text{m}}{\text{n}}\Big)^3=-\frac{\text{m}^3}{\text{n}^3}$
$\therefore\Big(-\frac{13}{8}\Big)^3$
$=-\Big(\frac{13}{8}\Big)^3$
$=-\Big(\frac{13^3}{8^3}\Big)$
$=-\Big(\frac{13\times13\times13}{8\times8\times8}\Big)$
$=-\frac{2197}{512}$
$\therefore\Big(-\frac{13}{8}\Big)^3$
$=-\Big(\frac{13}{8}\Big)^3$
$=-\Big(\frac{13^3}{8^3}\Big)$
$=-\Big(\frac{13\times13\times13}{8\times8\times8}\Big)$
$=-\frac{2197}{512}$
Question 981 Mark
Find the cube of:
$\frac{12}{7}$
$\frac{12}{7}$
Answer
View full question & answer→$\because\Big(\frac{\text{m}}{\text{n}}\Big)^3=\frac{\text{m}^3}{\text{n}^3}$
$\therefore\Big(\frac{12}{7}\Big)^3$
$=\frac{12^3}{7^3}$
$=\frac{12\times12\times12}{7\times7\times7}$
$=\frac{1728}{343}$
$\therefore\Big(\frac{12}{7}\Big)^3$
$=\frac{12^3}{7^3}$
$=\frac{12\times12\times12}{7\times7\times7}$
$=\frac{1728}{343}$
Question 991 Mark
Find the cube of:
$3\frac{1}{4}$
$3\frac{1}{4}$
Answer
View full question & answer→We have:
$3\frac{1}{4}=\frac{13}{4}$
$\because\Big(\frac{\text{m}}{\text{n}}\Big)^3=\frac{\text{m}^3}{\text{n}^3}$
$\therefore\Big(\frac{13}{4}\Big)^3$
$=\frac{13^3}{4^3}$
$=\frac{13\times13\times13}{4\times4\times4}$
$=\frac{2197}{64}$
$3\frac{1}{4}=\frac{13}{4}$
$\because\Big(\frac{\text{m}}{\text{n}}\Big)^3=\frac{\text{m}^3}{\text{n}^3}$
$\therefore\Big(\frac{13}{4}\Big)^3$
$=\frac{13^3}{4^3}$
$=\frac{13\times13\times13}{4\times4\times4}$
$=\frac{2197}{64}$
Question 1001 Mark
Find the cube of:
$2\frac{2}{5}$
$2\frac{2}{5}$
Answer
View full question & answer→We have:
$2\frac{2}{5}=\frac{12}{5}$
Also, $\because\Big(\frac{\text{m}}{\text{n}}\Big)^3=\frac{\text{m}^3}{\text{n}^3}$
$\therefore\Big(\frac{12}{5}\Big)^3$
$=\Big(\frac{12^3}{5^3}\Big)$
$=\frac{12\times12\times12}{5\times5\times5}$
$=\frac{1728}{125}$
$2\frac{2}{5}=\frac{12}{5}$
Also, $\because\Big(\frac{\text{m}}{\text{n}}\Big)^3=\frac{\text{m}^3}{\text{n}^3}$
$\therefore\Big(\frac{12}{5}\Big)^3$
$=\Big(\frac{12^3}{5^3}\Big)$
$=\frac{12\times12\times12}{5\times5\times5}$
$=\frac{1728}{125}$
Question 1011 Mark
Find the cube of:
2.1
2.1
Answer
View full question & answer→We have:
$2.1=\frac{21}{10}$
Also, $\Big(\frac{\text{m}}{\text{n}}\Big)^3=\frac{\text{m}^3}{\text{n}^3}$
$\therefore\Big(\frac{21}{10}\Big)^3$
$=\frac{21^3}{10^3}$
$=\frac{21\times21\times21}{10\times10\times10}$
$=\frac{9261}{1000}$
$=9.261$
$2.1=\frac{21}{10}$
Also, $\Big(\frac{\text{m}}{\text{n}}\Big)^3=\frac{\text{m}^3}{\text{n}^3}$
$\therefore\Big(\frac{21}{10}\Big)^3$
$=\frac{21^3}{10^3}$
$=\frac{21\times21\times21}{10\times10\times10}$
$=\frac{9261}{1000}$
$=9.261$
Question 1021 Mark
Find the cube of:
-21
-21
Answer
View full question & answer→Cube of -21 is given as:
(-21)3 = -21 × -21 × -21 = -9261
Thuse, the of -21 is (-9261)
(-21)3 = -21 × -21 × -21 = -9261
Thuse, the of -21 is (-9261)
Question 1031 Mark
Find the cube of:
1.5
1.5
Answer
View full question & answer→We have:
$1.5=\frac{15}{10}$
Also, $\Big(\frac{\text{m}}{\text{n}}\Big)^3=\frac{\text{m}^3}{\text{n}^3}$
$\therefore\Big(\frac{15}{10}\Big)^3$
$=\frac{15^3}{10^3}$
$=\frac{15\times15\times15}{10\times10\times10}$
$=\frac{3375}{1000}$
$=3.375$
$1.5=\frac{15}{10}$
Also, $\Big(\frac{\text{m}}{\text{n}}\Big)^3=\frac{\text{m}^3}{\text{n}^3}$
$\therefore\Big(\frac{15}{10}\Big)^3$
$=\frac{15^3}{10^3}$
$=\frac{15\times15\times15}{10\times10\times10}$
$=\frac{3375}{1000}$
$=3.375$
Question 1041 Mark
Find the cube of:
-12
-12
Answer
View full question & answer→Cube of -12 is given as:
(-12)3 = -12 × -12 × -12 = -1728
Thuse, the of -12 is (-1728)
(-12)3 = -12 × -12 × -12 = -1728
Thuse, the of -12 is (-1728)
Question 1051 Mark
Find the cube of:
-11
-11
Answer
View full question & answer→Cube of -11 is given as:
(-11)3 = -11 × -11 × -11 = -1331
Thuse, the of 11 is (-1331)
(-11)3 = -11 × -11 × -11 = -1331
Thuse, the of 11 is (-1331)
Question 1061 Mark
Find the cube of:
0.3
0.3
Answer
View full question & answer→We have:
$0.3=\frac{3}{10}$
Also, $\Big(\frac{\text{m}}{\text{n}}\Big)^3=\frac{\text{m}^3}{\text{n}^3}$
$\therefore\Big(\frac{3}{10}\Big)^3$
$=\frac{3^3}{10^3}$
$=\frac{3\times3\times3}{10\times10\times10}$
$-0.027$
$0.3=\frac{3}{10}$
Also, $\Big(\frac{\text{m}}{\text{n}}\Big)^3=\frac{\text{m}^3}{\text{n}^3}$
$\therefore\Big(\frac{3}{10}\Big)^3$
$=\frac{3^3}{10^3}$
$=\frac{3\times3\times3}{10\times10\times10}$
$-0.027$
Question 1071 Mark
Find the cube of:
0.08
0.08
Answer
View full question & answer→We have:
$0.08=\frac{8}{100}$
Also, $\Big(\frac{\text{m}}{\text{n}}\Big)^3=\frac{\text{m}^3}{\text{n}^3}$
$\therefore\Big(\frac{8}{100}\Big)^3$
$=\frac{8^3}{100^3}$
$=\frac{8\times8\times8}{100\times100\times100}$
$=\frac{512}{1000000}$
$=0.000512$
$0.08=\frac{8}{100}$
Also, $\Big(\frac{\text{m}}{\text{n}}\Big)^3=\frac{\text{m}^3}{\text{n}^3}$
$\therefore\Big(\frac{8}{100}\Big)^3$
$=\frac{8^3}{100^3}$
$=\frac{8\times8\times8}{100\times100\times100}$
$=\frac{512}{1000000}$
$=0.000512$
Question 1081 Mark
Evaluate the following:
$\sqrt[3]{\frac{729}{216}}\times\frac{6}{9}$
$\sqrt[3]{\frac{729}{216}}\times\frac{6}{9}$
Answer
View full question & answer→To 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.
$\sqrt[3]{\frac{729}{216}}\times\frac{6}{9}$
${\frac{\sqrt[3]{729}}{\sqrt[3]{216}}}\times\frac{6}{9}$
$=\frac{\sqrt[3]{9\times9\times9}}{\sqrt[3]{2\times2\times2\times3\times3\times3}}\times\frac{6}{9}$
$=\frac{9}{2\times3}\times\frac{6}{9}$
$=\frac{9^1}{6}\times\frac{6^1}{9}=1$
Thus, the answer is 1.
Question 1091 Mark
Evaluate:
$\sqrt[3]{8\times17\times17\times17}$
$\sqrt[3]{8\times17\times17\times17}$
Answer
View full question & answer→Property:
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:
$\sqrt[3]{8\times17\times17\times17}$
$=\sqrt[3]{2^3\times17^3}$
$=\sqrt[3]{2^3}\times\sqrt[3]{17^3}$
$=2\times17=34$
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:
$\sqrt[3]{8\times17\times17\times17}$
$=\sqrt[3]{2^3\times17^3}$
$=\sqrt[3]{2^3}\times\sqrt[3]{17^3}$
$=2\times17=34$
Question 1101 Mark
Evaluate:
$\sqrt[3]{4^3\times6^3}$
$\sqrt[3]{4^3\times6^3}$
Answer
View full question & answer→Property:
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:
$\sqrt[3]{-4^3\times6^3}$
$=\sqrt[3]{4^3}\times\sqrt[3]{6^3}$
$=4\times6=24$
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:
$\sqrt[3]{-4^3\times6^3}$
$=\sqrt[3]{4^3}\times\sqrt[3]{6^3}$
$=4\times6=24$