Question

What is the smallest number by which 4608 must be multiplied so that the product is a perfect cube? Also find the cube root so obtained

Answer 1

Factorisation of 4608 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3

= (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (3 × 3)

= 2³ × 2³ × 2³ × 3²

= 8 × 8 × 8 × 3²

= 8³ × 3²

∴ there is 3 required to form a cube of 3, 3 is the smallest number that should be multiplied by 3 to obtain a perfect cube.

4608 × 3 = 13824

∛13824 = 24