The smallest number by which 3645 must be multiplied so that it becomes perfect square is

The correct option is C $5$

$\begin{array}{cc}3& 3645\\ 3& 1215\\ 3& 405\\ 3& 135\\ 3& 45\\ 3& 15\\ 5& 5\\ & 1\end{array}$

Using prime factorization method we have,

$3645=3\times 3\times 3\times 3\times 3\times 3\times 5$

Grouping in pairs we get $(3\times 3)\times (3\times 3)\times (3\times 3)\times 5$

$\therefore$ We have to multiply $3645$ by $5$ to get a perfect square.