Answer
$10xy\sqrt{2y}$
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:
$=\sqrt{(50xy)(4xy^2)}
\\=\sqrt{200x^2y^3}$
Factor the radicand (expression inside the radical sign) so that at least one factor is a perfect square, and then simplify to obtain:
$=\sqrt{100x^2y^2(2y)}
\\=\sqrt{(10xy)^2(2y)}
\\=10xy\sqrt{2y}$
(There is no need for the absolute value since $x$ is a positive real number.)
