Chapter 9 - Roots and Radicals - 9.3 - More on Simplifying Radicals - Problem Set 9.3 - Page 412: 34

$\sqrt{3}$

Recall, we are not allowed to have radicals in the denominator of a fraction. Using the properties of radicals, the given expression, $ \dfrac{3\sqrt{2}}{\sqrt{6}} ,$ simplifies to \begin{array}{l}\require{cancel} 3\sqrt{\dfrac{2}{6}} \\\\= 3\sqrt{\dfrac{1}{3}} \\\\= 3\sqrt{\dfrac{1}{3}\cdot\dfrac{3}{3}} \\\\= 3\sqrt{\dfrac{3}{9}} \\\\= \dfrac{3\sqrt{3}}{\sqrt{9}} \\\\= \dfrac{3\sqrt{3}}{\sqrt{(3)^2}} \\\\= \dfrac{3\sqrt{3}}{3} \\\\= \dfrac{\cancel{3}\sqrt{3}}{\cancel{3}} \\\\= \sqrt{3} .\end{array}