Chapter 9 - Roots and Radicals - 9.3 - More on Simplifying Radicals - Problem Set 9.3 - Page 412: 27

$\dfrac{\sqrt{10}}{6}$

Recall, we are not allowed to have radicals in the denominator of a fraction. Using the properties of radicals, the given expression, $ \dfrac{\sqrt{5}}{\sqrt{18}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{\sqrt{5}}{\sqrt{18}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}} \\\\= \dfrac{\sqrt{10}}{\sqrt{36}} \\\\= \dfrac{\sqrt{10}}{\sqrt{(6)^2}} \\\\= \dfrac{\sqrt{10}}{6} .\end{array}