Chapter 9 - Roots and Radicals - 9.3 - More on Simplifying Radicals - Problem Set 9.3 - Page 412: 22

$\dfrac{\sqrt{21}}{6}$

Using the properties of radicals, the given expression, $ \sqrt{\dfrac{7}{12}} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt{\dfrac{7}{12}\cdot\dfrac{3}{3}} \\\\= \sqrt{\dfrac{21}{36}} \\\\= \dfrac{\sqrt{21}}{\sqrt{36}} \\\\= \dfrac{\sqrt{21}}{6} .\end{array}