Question

Which of the following numbers are not perfect cube?

(i) 512 (ii) 243 (iii) 1000

Answer 1

(i) 512 

Resolving 512 into Prime factors as follows

Here, all factors are in groups of three.

Therefore. 512 is a perfect cube.

(ii) 243 

Resolving 243 into Prime factors as follows

Here, 3 is not in groups of three. 

Therefore, 243 is not a perfect cube.

(iii) 1000

Resolving 1000 into prime factors as follows

Here, factors 2 and 5 are in groups of three.

Therefore, 1000 is not a perfect cube.