# Chapter 9 - Roots and Radicals - Chapter 9 Test - Page 431: 14

$3xy\sqrt{3x}$

#### Work Step by Step

Using the properties of radicals, the given expression, $\dfrac{3}{4}\sqrt{48x^3y^2} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{3}{4}\sqrt{16x^2y^2\cdot3x} \\\\= \dfrac{3}{4}\sqrt{(4xy)^2\cdot3x} \\\\= \dfrac{3}{4}\cdot4xy\sqrt{3x} \\\\= \dfrac{3}{\cancel{4}}\cdot\cancel{4}xy\sqrt{3x} \\\\= 3xy\sqrt{3x} .\end{array}

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