Which of the following numbers are not perfect cubes?
(i) 216 (ii) 128 (iii) 1000 (iv) 100 (v) 46656

Solution:

Cube root is the number that needs to be multiplied three times to get the original number.

For a number to be a perfect cube, all its prime factors should exist in triplets.

(i) 216

216 = 2 × 2 × 2 × 3 × 3 × 3

= 2³ × 3³

∴ 216 is a perfect cube

(ii) 128

128 = 2 × 2 × 2 × 2 × 2 × 2 × 2

= 2³ × 2³ × 2

∴ 128 is not a perfect cube

(iii) 1000

1000 = 2 × 2 × 2 × 5 × 5 × 5

= 2³ × 5³

∴ 1000 is a perfect cube

(iv) 100

100 = 2 × 2 × 5 × 5

= 2² × 5²

∴ 100 is not a perfect cube

(v) 46656

46656 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3

= 2³ × 2³ × 3³ × 3³

∴ 46656 is a perfect cube

☛ Check: NCERT Solutions for Class 8 Maths Chapter 7

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Video Solution:

Which of the following numbers are not perfect cubes? (i) 216 (ii) 128 (iii) 1000 (iv) 100 (v) 46656

NCERT Solutions for Class 8 Maths Chapter 7 Exercise 7.1 Question 1

Summary:

The numbers that are not perfect cubes among the given numbers (i) 216 (ii) 128 (iii) 1000 (iv) 100 (v) 46656 are 128 and 100

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