Chapter 9 - Roots and Radicals - 9.3 - More on Simplifying Radicals - Problem Set 9.3 - Page 412: 20

$\dfrac{\sqrt{10}}{5}$

Using the properties of radicals, the given expression, $ \sqrt{\dfrac{2}{5}} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt{\dfrac{2}{5}\cdot\dfrac{5}{5}} \\\\= \sqrt{\dfrac{10}{25}} \\\\= \dfrac{\sqrt{10}}{\sqrt{25}} \\\\= \dfrac{\sqrt{10}}{5} .\end{array}