Question

How to find sqare root by prime factorization.

Answer 1

The most common method to find the square root is Prime factorization
Eg- sq. root of 144
$\begin{array}{cc}2& 144\\ 2& 72\\ 2& 36\\ 2& 18\\ 3& 9\\ 3& 3\\ & 1\end{array}$
$\therefore 144=2^4\times 3^2\Rightarrow \sqrt{144}=\sqrt{2^4\times 3^2}{2}^2\times 3^1=4\times 3=12$