Answer
$$\dfrac{2\sqrt2}{|x|}$$
Work Step by Step
RECALL:
(1) For any real numbers $a \ge 0, b\ge0$, $\sqrt{ab}=\sqrt{a} \cdot \sqrt{b}$
(2) For any real numbers $a \ge 0, b\gt 0$, $\sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}$
(3) $\sqrt{a^2}=|a|$
Thus, using rule (2) above gives:
\begin{align*}
\sqrt{\dfrac{8}{x^2}}&=\dfrac{\sqrt8}{\sqrt{x^2}}\\\\
&=\dfrac{\sqrt{4(2)}}{\sqrt{x^2}}
\end{align*}
Using rule (1) above gives:
\begin{align*}
\dfrac{\sqrt{4(2)}}{\sqrt{x^2}}&=\dfrac{\sqrt4 \cdot \sqrt2}{\sqrt{x^2}}\\\\
&=\dfrac{2\sqrt2}{x^2}
\end{align*}
Using rule (3) above gives:
\begin{align*}
\dfrac{2\sqrt2}{\sqrt{x^2}}&=\dfrac{2\sqrt2}{|x|}
\end{align*}
