# Chapter 8 - Section 8.2 - Multiplying and Dividing Radicals - Exercise Set - Page 585: 57

$5\sqrt{2xy}$

#### Work Step by Step

Using $\sqrt{x}\cdot\sqrt{y}=\sqrt{xy}$ or the product rule of radicals, the given expression, $\sqrt{5x}\cdot\sqrt{10y} ,$ is equivalent to \begin{array}{l}\require{cancel} \sqrt{5x(10y)} \\\\= \sqrt{5x(2\cdot5\cdot y)} \\\\= \sqrt{(5)^2\cdot 2xy} \\\\= 5\sqrt{2xy} .\end{array} Note that variables are assumed to have positive real numbers.

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