Answer
$\dfrac{\sqrt{2xy}}{4y}$
Work Step by Step
Multiplying by an expression equal to $1$ which will make the denominator a perfect power of the index results to
\begin{array}{l}\require{cancel}
\sqrt{\dfrac{x}{8y}}
\\\\=
\sqrt{\dfrac{x}{8y}\cdot\dfrac{2y}{2y}}
\\\\=
\sqrt{\dfrac{1}{16y^2}\cdot2xy}
\\\\=
\sqrt{ \left( \dfrac{1}{4y} \right)^2\cdot2xy}
\\\\=
\dfrac{1}{4y}\sqrt{2xy}
\\\\=
\dfrac{\sqrt{2xy}}{4y}
.\end{array}
