# Chapter 9 - Roots and Radicals - 9.3 - More on Simplifying Radicals - Problem Set 9.3 - Page 412: 30

$\dfrac{\sqrt{3}}{4}$

#### Work Step by Step

Recall, we are not allowed to have radicals in the denominator of a fraction. Using the properties of radicals, the given expression, $\dfrac{\sqrt{9}}{\sqrt{48}} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt{\dfrac{9}{48}} \\\\= \sqrt{\dfrac{\cancel{3}\cdot3}{\cancel{3}\cdot16}} \\\\= \sqrt{\dfrac{3}{16}} \\\\= \dfrac{\sqrt{3}}{\sqrt{16}} \\\\= \dfrac{\sqrt{3}}{\sqrt{(4)^2}} \\\\= \dfrac{\sqrt{3}}{4} .\end{array}

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