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Question

Find the smallest number by which 2560 must be multiplied so that the product is a perfect cube.

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Solution

Factorising 2560 into prime factors.


2560=¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯2×2×2ׯ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯2×2×2ׯ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯2×2×2×5
Making them in groups of 3 equal factors, we are left 5
To make it into a group of 3, we have to multiply it by 5×5 i.e. by 25.
Hence, the smallest number by which it is multiplied = 25


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