## Introductory Algebra for College Students (7th Edition)

$10xy\sqrt{2y}$
Using $\sqrt{x}\cdot\sqrt{y}=\sqrt{xy}$ or the product rule of radicals, the given expression, $\sqrt{50xy}\cdot\sqrt{4xy^2} ,$ is equivalent to \begin{array}{l}\require{cancel} \sqrt{50xy(4xy^2)} \\\\= \sqrt{200x^2y^3} \\\\= \sqrt{100x^2y^2\cdot2y} \\\\= \sqrt{(10xy)^2\cdot2y} \\\\= 10xy\sqrt{2y} .\end{array} Note that variables are assumed to have positive real numbers.