# Chapter 9 - Roots and Radicals - 9.2 - Simplifying Radicals - Problem Set 9.2: 47

$\dfrac{2}{3}\sqrt{6xy}$

#### Work Step by Step

Using the properties of radicals, the given expression, $\dfrac{2}{9}\sqrt{54xy} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{2}{9}\sqrt{9\cdot6xy} \\\\= \dfrac{2}{9}\sqrt{(3)^2\cdot6xy} \\\\= \dfrac{2}{9}\cdot3\sqrt{6xy} \\\\= \dfrac{2}{\cancel{3}\cdot3}\cdot\cancel{3}\sqrt{6xy} \\\\= \dfrac{2}{3}\sqrt{6xy} .\end{array} Note that all of the variables are assumed to represent non-negative real numbers.

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