Question

What is the smallest number by which 17496 must be multiplied to obtain a perfect cube. Find the cube root of the number obtained

Answer 1

Prime factorisation of 17496 =

$2 {}^{3} \times 3 ^{3} \times 3 {}^{3} \times 3$

Therefore to get a perfect cube we should multiply it by 3×3 , i.e, 9

The number obtained =17496×9

=157464

Cube root of the number obtained

=2×3×3×3

=54

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