Chapter 9 - Roots and Radicals - 9.3 - More on Simplifying Radicals - Problem Set 9.3 - Page 412: 21

$\dfrac{\sqrt{10}}{4}$

Using the properties of radicals, the given expression, $ \sqrt{\dfrac{5}{8}} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt{\dfrac{5}{8}\cdot\dfrac{2}{2}} \\\\= \sqrt{\dfrac{10}{16}} \\\\= \dfrac{\sqrt{10}}{\sqrt{16}} \\\\= \dfrac{\sqrt{10}}{4} .\end{array}