by what smallest number should 34992 be multiplied so that the product

1.	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» $Resolving \:34992 \: into \:prime \:factors, we$ $get$ 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 $\red{Required \: <klux>PERFECT</klux> \:cube }$ $= 34992× 36$ $= 2^{3} \times 2^{3} \times 3^{3} \times 3^{3} \times 3^{3}$ $= ( 2 \times 2 \times 3 \times 3 \times 3 )^{3}$ $= (108)^{3} \: \blue {( Perfect \:cube )}$ $\red{ Cube \:root \: of \: (108)^{3} }\green { = 108 }$ •••♪