Chapter 9 - Roots and Radicals - 9.3 - More on Simplifying Radicals - Problem Set 9.3 - Page 412: 32

$\dfrac{\sqrt{3}}{6}$

Recall, we are not allowed to have radicals in the denominator of a fraction. Using the properties of radicals, the given expression, $ \sqrt{\dfrac{1}{12}} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt{\dfrac{1}{12}\cdot\dfrac{3}{3}} \\\\= \sqrt{\dfrac{3}{36}} \\\\= \dfrac{\sqrt{3}}{\sqrt{36}} \\\\= \dfrac{\sqrt{3}}{\sqrt{(6)^2}} \\\\= \dfrac{\sqrt{3}}{6} .\end{array}