Answer
$\dfrac{\sqrt{10xy}}{5y}$
Work Step by Step
Using the properties of radicals, the given expression, $
\dfrac{\sqrt{2x}}{\sqrt{5y}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt{2x}}{\sqrt{5y}}\cdot\dfrac{\sqrt{5y}}{\sqrt{5y}}
\\\\=
\dfrac{\sqrt{2x(5y)}}{(\sqrt{5y})^2}
\\\\=
\dfrac{\sqrt{10xy}}{5y}
.\end{array}
Note that all variables are assumed to represent positive real numbers.
