Answer
$5xy\sqrt{2y}$
Work Step by Step
Using $\sqrt{x}\cdot\sqrt{y}=\sqrt{xy}$ or the product rule of radicals, the given expression, $
\sqrt{5xy}\cdot\sqrt{10xy^2}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\sqrt{5xy(10xy^2)}
\\\\=
\sqrt{50x^2y^3}
\\\\=
\sqrt{25x^2y^2\cdot2y}
\\\\=
\sqrt{(5xy)^2\cdot2y}
\\\\=
5xy\sqrt{2y}
.\end{array}
Note that variables are assumed to have positive real numbers.
