Answer
$\dfrac{\sqrt{3x}}{8}$
Work Step by Step
Simplify the numerator to obtain:
\begin{align*}
\dfrac{\sqrt{3x^5}}{8x^2}&=\dfrac{\sqrt{(3x)(x^4)}}{8x^2}\\\\
&=\dfrac{\sqrt{(3x)(x^2)^2}}{8x^2}
\end{align*}
Use the rule $\sqrt{a^2}=|a|$ where $a=x^2$ to obtain:
\begin{align*}
\dfrac{\sqrt{(3x)(x^2)^2}}{8x^2}&=\dfrac{|x^2|\sqrt{3x}}{8x^2}
\end{align*}
The value of $x^2$ is never negative hence, $|x^2|=x^2$.
Thus,
\begin{align*}
\require{cancel}
\dfrac{|x^2|\sqrt{3x}}{8x^2}&=\dfrac{x^2\sqrt{3x}}{8x^2}\\\\
&=\dfrac{\cancel{x^2}\sqrt{3x}}{8\cancel{x^2}}\\\\
&=\dfrac{\sqrt{3x}}{8}
\end{align*}
