# Chapter 9 - Roots and Radicals - Chapter 9 Review Problem Set - Page 430: 35

$\dfrac{3\sqrt{xy}}{4y^2}$

#### Work Step by Step

Using the properties of radicals, the given expression, $\dfrac{3\sqrt{x}}{4\sqrt{y^3}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{3\sqrt{x}}{4\sqrt{y^2\cdot y}} \\\\= \dfrac{3\sqrt{x}}{4\sqrt{(y)^2\cdot y}} \\\\= \dfrac{3\sqrt{x}}{4y\sqrt{y}} \\\\= \dfrac{3\sqrt{x}}{4y\sqrt{y}}\cdot\dfrac{\sqrt{y}}{\sqrt{y}} \\\\= \dfrac{3\sqrt{xy}}{4y\cdot y} \\\\= \dfrac{3\sqrt{xy}}{4y^2} .\end{array} Note that all variables are assumed to have positive values.

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