Question

Which of the following is  perfect cube? 

 64

Answer 1

On factorising 64 into prime factors, we get

\[64 = 2 \times 2 \times 2 \times 2 \times 2 \times 2\]

Group the factors in triples of equal factors as:

\[64 = \left\{ 2 \times 2 \times 2 \right\} \times \left\{ 2 \times 2 \times 2 \right\}\]

It is evident that the prime factors of 64 can be grouped into triples of equal factors and no factor is left over. Therefore, 64 is a perfect cube.