# Chapter 10 - Exponents and Radicals - 10.4 Dividing Radical Expressions - 10.4 Exercise Set: 64

$\dfrac{15}{\sqrt{30}}$

#### Work Step by Step

Rationalizing the numerator, the given expression, $\dfrac{3\sqrt{10}}{2\sqrt{3}} ,$ is equivalent to \begin{array}{l} \dfrac{3\sqrt{10}}{2\sqrt{3}}\cdot\dfrac{\sqrt{10}}{\sqrt{10}} \\\\= \dfrac{3\sqrt{10^2}}{2\sqrt{30}} \\\\= \dfrac{3(10)}{2\sqrt{30}} \\\\= \dfrac{30}{2\sqrt{30}} \\\\= \dfrac{15}{\sqrt{30}} .\end{array}

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