__EXERCISE 4 (A)__

#### Question 1

### Write (T) for True or (F) for false:

**(i) The cube root of 8000 is 200.**

Sol: False

**(ii) Each prime factor appears 3 times in its cube.**

Sol: True

**(iii) .**

Sol: False

**(iv) For an integer a, is always greater than .**

Sol: False

**(v) The least number by which 72 must be divided to make it a perfect cube is 9.**

Sol: True

#### Question 2

### Find the cubes of the following numbers.

**(i) 8**

Sol: 8×8×8

=512

**(ii) -15**

Sol: (-15)×(-15)×(-15)

= -3375

**(iii) 600**

Sol:600×600×600

= 216000000

#### Question 3

**(i) **

Sol:

**(ii) **

Sol:

=

**(iii) **

Sol:

=

#### Question 4

**(i) 0.03**

Sol: 0.03×0.03×0.03

=

**(ii) 1.7**

Sol: 1.7×1.7×1.7

=

**(iii) -0.008**

Sol: -0.008×0.008×0.008

=

#### Question 5

### Which of the following numbers are perfect cubes?

**65, 128, 243, 512, 900, 1728, 4096**

Sol:

#### Question 6

### Find the cube root of the following numbers by prime factorization method.

**(i) 5832**

Sol:

**(ii) 91125 **

Sol:

**(iii) -9261**

Sol:

**(iv) **

Sol:

**(v) **

Sol:

**(vi) **

Sol:

#### Question 7

### Evaluate:

**(i) **

Sol:

**(ii) **

Sol:

#### Question 8

### What is the smallest number by which each of the following numbers must be multiplied so that the product is a perfect cube.Also, find cube root of the product.

**(i) 1125**

Sol:

**(ii) 6912**

Sol:

**(iii) 47916**

Sol:

#### Question 9

### Find the smallest number by which each of the following numbers must be divided so that quotient is a perfect cube. Also, find the cube root of the product.

**(i) 3584**

Sol:

**(ii) 1458**

Sol:

**(iii) 120393**

Sol:

#### Question 10

**Find the value of :**

**(i) **

**(ii) **

**(iii) **