Question 511 Mark
Find the cube of the following numbers:
$21$
$21$
Answer
View full question & answer→Cube of $21=21^3=21 \times 21 \times 21=9261$
Questions · Page 2 of 3
1 Marks Question
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, $\because\Big(\frac{\text{m}}{\text{n}}\Big)^3=\frac{\text{m}^3}{\text{n}^3}$
$\therefore\Big(\frac{12}{5}\Big)^3$
$=\Big(\frac{12^3}{5^3}\Big)$
$=\frac{12\times12\times12}{5\times5\times5}$
$=\frac{1728}{125}$