Question

For the following number, find the smallest whole number by which it should be multiplied so as to get a perfect square number.
$1008$

Answer 1

By prime factorization of $1008$, we get

$1008=2\times 2\times 2\times 2\times 3\times 3\times 7$

Here $2$ and $3$ are in pair, but $7$ needs a pair to make $1008$ a perfect square.

Thus $1008$ needs to be multiplied by $7$ to become a perfect square.