# NCERT Class 8 Mathematics Solutions: Chapter 7 – Cubes and Cube Roots Exercise 7.1 Part 1

Question: 1 Which of the following numbers are not perfect cubes:

(i) 216

(ii) 128

(iii) 1000

(iv) 100

(v) 46656

(iv) 100

(i) 216

 2 216 2 108 2 54 3 27 3 9 3 3 1

Prime factors of 216 =

Here all factors are in groups of 3’s (in triplets)

Therefore, 216 is a perfect cube number.

(ii) 128

 2 128 2 64 2 32 2 16 2 8 2 4 2 2 1

Prime factors of

Here one factor 2 does not appear in a 3’s group.

Therefore, 128 is not a perfect cube.

(iii) 1000

 2 1000 2 500 2 250 5 125 5 25 5 5 1

Prime factors of 1000

Here all factors appear in 3’s group.

Therefore, 1000 is not a perfect cube.

(iv) 100

 2 100 2 50 5 25 5 5 1

Prime factors of 100

Here all factors do not appear in 3’s group.

Therefore, 100 is not a perfect cube.

(v) 46656

 2 46656 2 23328 2 11664 2 5832 2 2916 2 1458 3 729 3 243 3 81 3 27 3 9 3 3 1

Prime factors of

Here, all factors appear in 3’s group.

Therefore, 46656 is a perfect cube.