## RS Aggarwal Class 8 solutions Chapter 4 Cubes and Cube Roots Ex 4A in pdf free download

Contents

**Question 1.**

**Evaluate :**

**(i) (8)³**

**(ii) (15)³**

**(iii) (21)³**

**(iv) (60)³**

**Solution:**

(i) (8)³ = 8 x 8 x 8 = 512

(ii) (15)³ = 15 x 15 x 15 = 3375

(iii) (21)³ = 21 x 21 x 21 = 9261

(iv) (60)³ = 60 x 60 x 60 = 216000 Ans.

**Question 2.**

**Evatuate :**

**(i) (1.2)³**

**(ii) (3.5)³**

**(iii) (o.8)³**

**(iv) (0.05)³**

**Solution:**

(i)(1.2)³= 1.2 x 1.2 x 1.2 = 1.728

(ii) (3.5)³ = 3.5 x 3.5 x 3.5 = 42.875

(iii) (0.8)³ = 0.8 x 0.8 x 0.8 = 0.512

(iv) (0.05)³ = 0.05 x 0.05 x 0.05 = 0.000125

**Question 3.**

**Evatuate :**

**(a)**

**(b)**

**(c)**

**(d)**

**Solution:**

**Question 4.**

**Which of the following numbers are perfect cubes ? In case of perfect cube, find the number whose cube is the given number.**

**(i) 125**

**(ii) 243**

**(iii) 343**

**(iv) 256**

**(v) 8000**

**(vi) 9261**

**(vii) 5324**

**(viii) 3375**

**Solution:**

(i) 125

=

**Question 5.**

**Which of the following are the cubes of even numbers?**

**(i) 216**

**(ii) 729**

**(iii) 512**

**(iv) 3375**

**(v) 1000**

**Solution:**

We know that cube of an even number is also even.

216, 1000 and 512 are the cubes of even numbers as these are all even numbers. Ans.

**Question 6.**

**Which of the following are the cubes of odd numbers?**

**(i) 125**

**(ii) 343**

**(iii) 1728**

**(iv) 4096**

**(v) 9261**

**Solution:**

We know that cube of an odd number is also odd.

125, 343 and 9261 are the cubes of odd natural numbers as these are also odd numbers. Ans.

**Question 7.**

**Find the smallest number by which 1323 must be multiplied so that the product is a perfect cube.**

**Solution:**

Factorising 1323 into prime factors,

**Question 8.**

**Find the smallest number by which 2560 must be multiplied so that the product is a perfect cube.**

**Solution:**

Factorising 2560 into prime factors.

Making them in groups of 3 equal factors, we are left 5

To make it into a group of 3, we have to multiply it by 5 x 5 i.e. by 25.

Hence, the smallest number by which it is multiplied = 25 Ans.

**Question 9.**

**What is the smallest number by which 1600 must be divided so that the quotient is a perfect cube?**

**Solution:**

Factorising 1600 into prime factors

**Question 10.**

**Find the smallest number by which 8788 must be divided so that the quotient is a perfect cube.**

**Solution:**

Factorising 8788 into prime factors

Making them in groups of 3 equal factors, we are left with 2 x 2

2 x 2 i.e. 4 is to be divided.

Hence least number to be divided for getting perfect cube = 4 Ans.

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