Answer
$5\sqrt{2xy}$
Work Step by Step
Using $\sqrt{x}\cdot\sqrt{y}=\sqrt{xy}$ or the product rule of radicals, the given expression, $
\sqrt{5x}\cdot\sqrt{10y}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\sqrt{5x(10y)}
\\\\=
\sqrt{5x(2\cdot5\cdot y)}
\\\\=
\sqrt{(5)^2\cdot 2xy}
\\\\=
5\sqrt{2xy}
.\end{array}
Note that variables are assumed to have positive real numbers.
