S.chand Class 8 Maths Solution Chapter 4 Cubes and Cube roots Exercise 4

 Exercise 4

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Q1 | Ex-4 | Cubes and Cube roots |Class 8 | Schand Composite Mathematics| Chapter 4 | myhelper

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Question 1

Find the cubes of the following numbers :

(i) 13

(ii) 400

(iii) $\frac{-4}{9}$

(iv) $2 \frac{5}{7}$

(v) 0.3

(vi) 0.08

(vii) -2.4

(viii) 0.001

Sol :

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Question 2

Which of the following numbers are perfect cubes ?

64,125,243,729,1331,864,4096,74088

Sol :

Sol :

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Question 3

What is the smallest number by which 675 should be multiplied so that the product is a perfect cube ?

Sol :

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Question 4

What is the smallest number by which 2916 should be divided so that the quotient is a perfect cube ?

Sol :

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Question 5

Write cubes of five natural numbers which are multiples of 3 and verify the following :

'The cube of a natural number which is a multiple of 3 is a multiple of 27 '.

Sol :

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Question 6

Find the cube roots of the following numbers by prime factorisation method :

(i) 125

(ii) 343

(iii) 2744

(iv) 3375

(v) $-729$

(vi) $-1728$

(vii) $\frac{-3375}{4913}$

(viii) $5 \frac{23}{64}$

Sol :

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Question 7

Evaluate :

(i) $\sqrt[3]{0.216}$

(ii) $\sqrt[3]{4.096}$

(iii) $\sqrt[3]{0.003375}$

Sol :

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Question 8

Show that $\sqrt[3]{27} \times \sqrt[3]{125}=\sqrt[3]{27 \times 125}$.

Sol :

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Question 9

Find the value of 

(i) $\sqrt[3]{392} \times \sqrt[3]{448}$

(ii) $\sqrt[3]{3375 \times 729}$

Sol :

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Question 10

Find the smallest number by which 17496 must be divided, so that the quotient is a perfect cube. Also find the cube root of the quotient.

Sol :

Multiple Choice Questions (MCQs)

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Question 11

The digit in the units place of the cube of 47 is :

(a) 9

(b) 7

(c) 3

(d) 1

Sol :

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Question 12

The least possible value of A for which 90×A is a perfect cube is

(a) 200

(b) 300

(c) 500

(d) 600

Sol :

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Question 13

$\sqrt[3]{5-\frac{10}{27}}$ is

(a) $\frac{4}{3}$

(b) $\frac{3}{4}$

(c) $\frac{5}{3}$

(d) $\frac{3}{5}$

Sol :

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Question 14

$\sqrt[3]{-1728}+\sqrt{324}=$

(a) 30

(b) 6

(c) 4

(d) 32

Sol :

High Order Thinking Skills (HOTS)

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Question 15

Evaluate : $\sqrt[3]{\sqrt{0.000729}}+\sqrt[3]{0.008}$

Sol :