Question

Which of the following is  perfect cube? 

1000

Answer 1

On factorising 1000 into prime factors, we get:

\[1000 = 2 \times 2 \times 2 \times 5 \times 5 \times 5\]

Group the factors in triples of equal factors as:

\[1000 = \left\{ 2 \times 2 \times 2 \right\} \times \left\{ 5 \times 5 \times 5 \right\}\]

It is evident that the prime factors of 1000 can be grouped into triples of equal factors and no factor is left over. Therefore, 1000 is a perfect cube.