Answer
$ \frac{a}{2}\sqrt{\frac{5 a b}{x}} $
Work Step by Step
Given\begin{equation}
\sqrt{\frac{10 a^3 b}{8 x}}.
\end{equation} Simplify.
\begin{equation}
\begin{aligned}
\sqrt{\frac{10 a^3 b}{8 x}}& =\sqrt{\frac{10 a^2\cdot a b}{4\cdot 2 x}} \\
& =\frac{a}{2}\sqrt{\frac{5 a b}{x}}.
\end{aligned}
\end{equation}
