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MATHS [2 Mark Question Answer]

Cubes and Cube Roots · ICSE STD 8 (ICSE - English Medium). 35 questions.

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[2 Mark Question Answer]

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35 questions · timed · auto-graded

Question 12 Marks
Find the cube$-$root of $\frac{729}{-1331}$
Answer
$ \frac{729}{-1331}$
$ =\frac{(9 \times 9 \times 9)}{-(11 \times 11 \times 11)}$
$ =-\frac{9}{11}$
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Question 22 Marks
Find the cube$-$root of $-\frac{27}{343}$
Answer
$ \frac{27}{343}$
$ =\frac{3 \times 3 \times 3}{7 \times 7 \times 7}$
$ =-\frac{3}{7}$
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Question 32 Marks
Find the cube$-$root of $ -64 x -125$
Answer
$-64 \times -125$
$= -(4 \times 4 \times 4) \times -(5 \times 5 \times5)$
$= -4 \times -5$
$= 20$
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Question 42 Marks
Find the cube$-$root of $-125 \times 1000$
Answer
$ -125 \times 1000$
$ =\sqrt{-125 \times 100}$
$ =\sqrt{-(5 \times 5 \times 5) \times(10 \times 10 \times 10)}$
$ =-5 \times 10$
$ =-50$
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Question 52 Marks
Find the cube$-$root of $-0.512$
Answer
$ -0.512$
$ =\sqrt[3]{\frac{-512}{1000}}$
$ =\sqrt{\frac{-8 \times-8 \times-8}{10 \times 10 \times 10}}$
$ =\frac{-8}{10}$
$ =-0.8$
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Question 62 Marks
Find the cube$-$root of $0.000027$
Answer
$ 0.000027$
$ =\sqrt[3]{\frac{27}{1000000}}$
$ =\sqrt[3]{\frac{3 \times 3 \times 3}{100 \times 100 \times 100}}$
$ =\frac{3}{100}$
$ =0.03$
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Question 72 Marks
Find the cube$-$ root of $-2197.$
Answer
$\begin{aligned} & -2197 \\ & =\sqrt[3]{-2197}\end{aligned}$
$13$ $2197$
$13$ $169$
$13$ $13$
  $1$
$\begin{aligned} & =\sqrt[3]{-13 \times-13 \times-13} \\ & =-13\end{aligned}$
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Question 82 Marks
Find the cube$-$root of $\frac{-512}{343}$
Answer
$ \frac{-512}{343}$
$ =-\sqrt[3]{\frac{512}{343}}$
$ =-\sqrt[3]{\frac{8 \times 8 \times 8}{7 \times 7 \times 7}}$
$ =-\frac{8}{7}$
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Question 92 Marks
Find the cube$-$root of $-\frac{64}{343}$
Answer
$ -\frac{64}{343}$
$ =\frac{\sqrt[3]{-64}}{\sqrt[3]{343}}$
$ =\frac{\sqrt[3]{-4 \times-4 \times-4}}{\sqrt[3]{7 \times 7 \times 7}}$
$ =\frac{-4}{7}$
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Question 102 Marks
Find the cube$-$root of $-\frac{27}{125}$
Answer
$ -\frac{27}{125}$
$ =-\frac{\sqrt{27}}{\sqrt{125}}$
$ =-\sqrt{\frac{3 \times 3 \times 3}{5 \times 5 \times 5}}$
$ =-\frac{3}{5}$
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Question 112 Marks
Find the cube$-$root of $-1331$
Answer
$ -1331$
$ =\sqrt[3]{-1331}$
$ =\sqrt{-11 \times-11 \times-11}$
$ =-11$
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Question 122 Marks
Find the cube$-$ root of$ -512$
Answer
$ -512$
$ =\sqrt[3]{-512}$
$ =\sqrt{-8 \times-8 \times-8}$
$ =-8$
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Question 142 Marks
Find the cube $-$root of $3375 \times 512$
Answer
$ 3375 \times 512$
$ =\sqrt[3]{3375 \times 512}$
$ =\sqrt{15 \times 15 \times 15 \times 8 \times 8 \times 8}$
$ =15 \times 8$
$ =120$
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Question 152 Marks
Find the cube$-$root of $729 \times 8000$
Answer
$ 729 \times 8000$
$ =\sqrt[3]{729 \times 8000}$
$ =\sqrt{9 \times 9 \times 9 \times 20 \times 20 \times 20}$
$ =9 \times 20$
$ =180$
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Question 162 Marks
Find the cube$-$root of $64 \times 27.$
Answer
$ 64 \times 27$
$ =\sqrt[3]{64 \times 27}$
$ =\sqrt{4 \times 4 \times 4 \times 3 \times 3 \times 3}$
$ =4 \times 3$
$ =12$
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Question 172 Marks
Find the cube $-$root of $64 \times 729$
Answer
$ 64 \times 729$
$ =\sqrt[3]{64 \times 729}$
$ =\sqrt{4 \times 4 \times 4 \times 9 \times 9 \times 9}$
$ =4 \times 9$
$ =36$
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Question 182 Marks
Find the cube$-$root of $\frac{343}{512}$
Answer
$ \frac{343}{512}$
$ =\sqrt[3]{\frac{343}{512}}$
$ =\frac{\sqrt{7 \times 7 \times 7}}{\sqrt{8 \times 8 \times 8}}$
$ =\frac{7}{8}$
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Question 192 Marks
Find the cube$-$root of $\frac{125}{216}$
Answer
$ \frac{125}{216}$
$ =\sqrt[3]{\frac{125}{216}}$
$ =\frac{\sqrt{5 \times 5 \times 5}}{\sqrt{6 \times 6 \times 6}}$
$ =\frac{5}{6}$
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Question 202 Marks
Find the cube$-$ root of $343$
Answer
$ 343$
$ =\sqrt[3]{343}$
$ =7 \times 7 \times 7=7$
$7$ $343$
$7$ $49$
$7$ $7$
  $1$
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Question 212 Marks
Find the cube $-$ root of $64$
Answer
$ 64$
$ =\sqrt[3]{64}$
$ =(2 \times 2 \times 2) \times(2 \times 2 \times 2)$
$ =2 \times 2$
$ =4$
$2$ $64$
$2$ $32$
$2$ $16$
$2$ $8$
$2$ $4$
$2$ $2$
  $1$
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Question 222 Marks
Find the least number by which $1323$ must be multiplied so that the product is a perfect cube.
Answer
The prime factor of $1323$ are $=3 \times 3 \times 3 \times 7 \times 7$
$= (3 \times 3 \times 3) \times 7 \times 7$
Clearly, $1323$ must be multiplied by $7$.
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Question 232 Marks
Find the cube of: $-50$
Answer
$-50$
$= (-50)^3$
$= (-50) \times (-50) \times (-50)$
$= -(50 \times 50 \times 50)$
$= -125000$
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Question 242 Marks
Find the cube of: $-30$
Answer
$-30$
$= (-30)^3$
$= (-30) \times (-30) \times (-30)$
$= -(30 \times 30 \times 30)$
$= -27000$
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Question 252 Marks
Find the cubes of: $-25$
Answer
$-25$
$= (-25)^3$
$= (-25) \times (-25) \times (-25)$
$= -(25 \times 25 \times 25)$
$= -15625$
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Question 262 Marks
Find the cube of: $-18$
Answer
$-18$
$= (-18)^3$
$= (-18) \times (-18)\times( -18)$
$= -(18 \times 18 \times 18)$
$= -5832$
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Question 272 Marks
Find the cube of: $-12$
Answer
$-12$
$= (-12)^3$
$= (-12) \times (-12) \times (-12)$
$= -(12 \times 12 \times 12)$
$= -1728$
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Question 282 Marks
Find the cube of: $-7$
Answer
$-7$
$= (-7)^3$
$= (-7) \times (-7) \times (-7)$
$= -(7 \times 7 \times 7)$
$=-343$
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Question 292 Marks
Find the cube of:$ -3$
Answer
$-3$
$= (-3)^3$
$=( -3) \times (-3) \times (-3)$
$= -(3 \times 3 \times 3)$
$= -27$
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Question 302 Marks
Find the cube of: $\frac{10}{13}$
Answer
$ \frac{10}{13}$
$ =\left(\frac{10}{13}\right)^3$
$ =\frac{10 \times 10 \times 10}{13 \times 13 \times 13}$
$ =\frac{1000}{2197}$
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Question 312 Marks
Find the cube of: $\frac{8}{9}$
Answer
$ \frac{8}{9}$
$ =\left(\frac{8}{9}\right)^3$
$ =\frac{8 \times 8 \times 8}{9 \times 9 \times 9}$
$ =\frac{512}{729}$
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Question 322 Marks
Find the cube of: $\frac{3}{7}$
Answer
$\frac{3}{7}$
$\begin{aligned} & =\left(\frac{3}{7}\right)^3 \\ & =\frac{3 \times 3 \times 3}{7 \times 7 \times 7}\end{aligned}$
$=\frac{27}{343}$
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Question 332 Marks
Find the cube of $1.6.$
Answer
$ 1.6$
$ =(1.6)^3=1.6 \times 1.6 \times 1.6$
$ =2.56 \times 1.6$
$ =4.096$
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Question 342 Marks
Find if the following number is a perfect cube. $1938$
Answer
$2$ $1938$
$3$ $969$
$17$ $323$
$19$ $19$
  $1$
$1938 = 2 × 3 × 17 × 19$
$∴ 1938 $ is not a perfect cube.
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Question 352 Marks
Find if the following number is a perfect cube? $588$
Answer
$588$
$2$ $588$
$2$ $294$
$7$ $147$
$7$ $21$
$3$ $3$
  $1$
$ 588 = 2 \times 2 \times 7 \times 7 \times 3$
$\therefore 588 $ is not perfect cube.
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