# How do you simplify sqrt(8x^2)?

Sep 28, 2015

$\sqrt{8 {x}^{2}} = 2 \sqrt{2} \left\mid x \right\mid$

#### Explanation:

$\sqrt{8 {x}^{2}}$
$\textcolor{w h i t e}{\text{XXX}} = \sqrt{{2}^{2} \cdot 2 \cdot {x}^{2}}$
$\textcolor{w h i t e}{\text{XXX}} = \sqrt{{2}^{2}} \cdot \sqrt{2} \cdot \sqrt{{x}^{2}}$
$\textcolor{w h i t e}{\text{XXX}} = 2 \sqrt{2} \left\mid x \right\mid$

Note, by convention, $\sqrt{q}$ for $q \in {\mathbb{R}}^{0 +}$ is the primary (non-negative) square root and therefore it is necessary to take the absolute value of $x$ when evaluating $\sqrt{{x}^{2}}$