Question

Find two smallest perfect squares whose product is a perfect cube.

Answer 1

The list of perfect cubes is given below.

1 = 1 × 1 × 1

8 = 2 × 2 × 2

27 = 3 × 3 × 3

It is seen that 64 = 4 × 16.

Here, 4 and 16 are perfect squares.

Thus, the required smallest perfect squares whose product is a perfect cube are 4 and 16.