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
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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
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