Question

Find the smallest number by which the following number must be multiplied to obtain a perfect cube: $100$.

Answer 1

Calculate the prime factorisation of $100$.

$100=2\times 2\times 5\times 5$

To make it a perfect cube, it should be multiplied by $5\times 2=10$.

$\begin{array}{rcl}& \Rightarrow & 100\times 10=2\times 2\times 5\times 5\times 10\\ & =& 2\times 2\times 2\times 5\times 5\times 5\end{array}$

which is a perfect cube of $10$.

Hence, the smallest number by which $100$ must be multiplied to obtain a perfect cube is $10$.