Question

by what smallest number should 34992 be multiplied so that the product becomes a perfect you also find the cube root of the product

Answer 1

$Resolving \:34992 \: into \:prime \:factors, we$

$get$

34992 = 2×2×2×2×3×3×3×3×3×3×3

The prime factors 2 and 3 doesn't appear in a group of three.

So, 34992 is not a perfect cube .

Hence, smallest number by which it is to be multiplied to make it a perfect cube is 2×2×3×3 = 36

$\red{Required \: perfect \:cube }$

$= 34992× 36$

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

$= ( 2 \times 2 \times 3 \times 3 \times 3 )^{3}$

$= (108)^{3} \: \blue {( Perfect \:cube )}$

$\red{ Cube \:root \: of \: (108)^{3} }\green { = 108 }$

•••♪