S.chand publication New Learning Composite mathematics solution of class 8 Chapter 3 Squares and Square roots,Cube and Cube roots Exercise 3E

 Exercise 3E

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Q1 |Ex-3E |Class 8 |Squares and Square roots,Cube ,Cube roots |S.Chand New Learning Composite

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Question 1

Find the cubes of the following numbers.

(a) 12³

Sol : 1728

(b) 15³

Sol : 3375

(c) 50³

Sol : 125000

(d) 200³

Sol : 8000000

(e) $\left(-\frac{3}{7}\right)^3$

Sol : $-\frac{27}{343}$

(f) $1\frac{3}{8}^3$

Sol : $\frac{11}{8}^3=\frac{1331}{512}$

(g) 0.4³

Sol : $=\frac{4}{10}=\frac{64}{1000}$

=0.064

(h) 0.9³

Sol : $=\frac{9}{10}^3=\frac{729}{1000}$

=0.729

(i) 0.02³

Sol : $=\frac{2}{100}^3=\frac{8}{1000000}$

=0.000008

(j) $-2\frac{2}{9}^3$

Sol : $-\frac{20^3}{9}=-\frac{8000}{729}$

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Q2 |Ex-3E |Class 8 |Squares and Square roots,Cube ,Cube roots |S.Chand New Learning Composite

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Question 2

Which of the following numbers are perfect cubes?

(a) 125

Sol : 5×5×5

[perfect cube]

(b) 2197

Sol : 13×13×13

[perfect cube]

(c) 832

Sol : 2×2×2×2×2×2×13

[not a perfect cube]

(d) 2744

Sol : 2×2×2×7×7×7

[perfect cube]

(e) 2000

Sol : 5×5×5×4×4

[not a perfect cube]

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Q3 |Ex-3E |Class 8 |Squares and Square roots,Cube ,Cube roots |S.Chand New Learning Composite

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Question 3

What is the smallest natural number by which the following should be multiplied so that they become perfect cubes?

(a) 36

Sol : 2×2×3×3

=2×3=6 need smallest natural number 6 for perfect cube

(b) 121

Sol : 11×11=11  need smallest natural number 11 for perfect cube

(c) 392

Sol : 2×2×2×7×7=7 need smallest natural number 7 for perfect cube

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Q4 |Ex-3E |Class 8 |Squares and Square roots,Cube ,Cube roots |S.Chand New Learning Composite

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Question 4

What is the smallest natural number by which the following numbers should be divided so that they become perfect cubes?

(a) 54

Sol : 2×3×3×3

divided by 2

(b) 625

Sol : 5×5×5×5

divided by 5

(c) 1536

Sol : 2×2×2×2×2×2×2×2×2×3

divided by 3

(d) 7000

Sol : 7×5×5×5×2×2×2

divided by 7

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Q5 |Ex-3E |Class 8 |Squares and Square roots,Cube ,Cube roots |S.Chand New Learning Composite

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Question 5

Find the cube root of each of the following numbers by prime factorisation method.

(a) 8

Sol : 2×2×2=2

(b) 216

Sol : 6×6×6=6

(c) 1728

Sol : 2×2×2×3×3×3=12

(d) $-4\frac{17}{27}$

Sol : $=-\frac{125}{27}=-\frac{5\times 5\times 5}{3\times 3\times 3}$

(e) 0.027

Sol : $=\frac{27}{1000}=\frac{3\times 3\times 3}{10\times 10\times 10}=\frac{3}{10}$

=0.3

(f) -.216

Sol : $=\frac{216}{1000}=\frac{6\times 6\times 6}{10\times 10\times 10}=\frac{6}{10}$

=06

(g) 0.001331

Sol : $=\frac{1331}{1000000}=\frac{11\times 11\times 11}{100\times 100\times 100}=\frac{11}{100}$

=0.11

(h) 0.002744

Sol : $=\frac{2744}{1000000}=\frac{14\times 14\times 14}{100\times 100\times 100}=\frac{14}{100}$

=0.14