#### Answer

$5xy\sqrt[]{10x}$

#### Work Step by Step

Extracting the factors that are perfect powers of the index, the given expression simplifies to
\begin{array}{l}\require{cancel}
\sqrt[]{250x^3y^2}
\\\\=
\sqrt[]{25x^2y^2\cdot10x}
\\\\=
\sqrt[]{(5xy)^2\cdot10x}
\\\\=
5xy\sqrt[]{10x}
.\end{array}
Note that all variables are assumed to represent positive numbers.