Question

Which of the following is  perfect cube? 

 4608

Answer 1

On factorising 4608 into prime factors, we get:

\[4608 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3\]

Group the factors in triples of equal factors as:

\[4608 = \left\{ 2 \times 2 \times 2 \right\} \times \left\{ 2 \times 2 \times 2 \right\} \times \left\{ 2 \times 2 \times 2 \right\} \times 3 \times 3\]

It is evident that the prime factors of 4608 cannot be grouped into triples of equal factors such that no factor is left over. Therefore, 4608 is a not perfect cube.