Answer
$4\sqrt{5xy}$
Work Step by Step
Using $\sqrt{x}\cdot\sqrt{y}=\sqrt{xy}$ or the product rule of radicals, the given expression, $
\sqrt{8x}\cdot\sqrt{10y}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\sqrt{8x(10y)}
\\\\=
\sqrt{80xy}
\\\\=
\sqrt{16\cdot5xy}
\\\\=
\sqrt{(4)^2\cdot5xy}
\\\\=
4\sqrt{5xy}
.\end{array}
Note that variables are assumed to have positive real numbers.
