Question

How do you simplify $\sqrt{8x^2}$?

Answer 1

Simplify $\sqrt{8x^2}$:

Factor out the expression $8x^2$.

$\begin{array}{rcl}8x^2& =& 4\times 2\times x^2\\ & =& 2^2\times 2\times x^2\end{array}$

Take the square root on both sides of the equation.

$\begin{array}{rcl}\sqrt{8x^2}& =& \sqrt{2^2\times 2\times x^2}\\ & =& \sqrt{2^2}\times \sqrt{2}\times \sqrt{x^2}\left(\because \sqrt{a\times b}=\sqrt{a}\times \sqrt{b}\right)\\ & =& 2\sqrt{2}\left|x\right|\end{array}$

Hence, the simplified form of $\sqrt{8x^2}$ is $2\sqrt{2}\left|x\right|$.