Question

How do you simplify the square root of $240$?

Answer 1

Find the square root of $\mathbf{240}$:

Prime factors of $240$ are $2\times 2\times 2\times 2\times 3\times 5$:

$240=2^4\times 3\times 5$.

Take square root on both sides:

$\begin{array}{rcl}\sqrt{240}& =& \sqrt{2^4\times 3\times 5}\\ & =& 2^2\sqrt{3\times 5}\\ & =& 4\sqrt{15}\end{array}$

Therefore, the square root of $\mathbf{240}$ is $\mathbf{4}\sqrt{\mathbf{15}}$.