#### Answer

$5xy\sqrt{2y}$

#### Work Step by Step

RECALL:
For any non-negative real numbers a and b,
$\sqrt[n]{a} \cdot \sqrt[n]{b} = \sqrt[n]{ab}$
Use the rule above to obtain:
$=\sqrt{(5xy)(10xy^2)}
\\=\sqrt{50x^2y^3}$
Factor the radicand (expression inside the radical sign) so that at least one factor is a perfect square, and then simplify to obtain:
$=\sqrt{25x^2y^2(2y)}
\\=\sqrt{(5xy)^2(2y)}
\\=5xy\sqrt{2y}$
(There is no need for the absolute value since $x$ is a positive real number.)