Answer
$5xy\sqrt{2x}$.
Work Step by Step
Use the product rule $\sqrt A\cdot \sqrt B=\sqrt{AB}$.
$\Rightarrow \sqrt{5xy}\cdot \sqrt{10x^2y}=\sqrt{5xy \cdot 10x^2y}$
Multiply.
$\Rightarrow \sqrt{50x^{1+2}y^{1+1}}$
$\Rightarrow \sqrt{50x^{3}y^{2}}$
Group the perfect square.
$\Rightarrow \sqrt{(5^2x^{2}y^{2})( 2x)}$
Factor into two radicals.
$\Rightarrow \sqrt{(5^2x^{2}y^{2})}\sqrt{( 2x)}$
Simplify.
$\Rightarrow 5xy\sqrt{2x}$.
