Chapter 7. Cubes and Cube Roots

Exercise 7.1

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

 By prime factorisation ,we have  

216=2×2×2×3×3×3 

The prime factor 2 and 3 are appeared in a group of three . So, 216 is a perfect cube .

(ii) 128

By prime factorisation ,we have 

128=2×2×2×2×2×2×2 

Since there is only one 2 in the prime factorisation . So, we need (2 × 2 =) 4 to make it a perfect cube .

Therefore, 128 is not a perfect cube .

(iii) 1000

By prime factorisation ,we have 

1000=2×2×2×5×5×5 

The prime factor 2 and 5 are appeared in a group of three . So, 1000 is a perfect cube .

(iv) 100

By prime factorisation ,we have 

100=2×2×5×5 

The prime factor 2 and 5 are not appeared in a group of three . So, 100 is not a perfect cube .

(v) 46656

By prime factorisation ,we have 

46656=2×2×2×2×2×2×3×3×3×3×3×3  

The prime factor 2 and 3 are appeared in a group of three . So, 46656 is a perfect cube .