Chapter 9 - Roots and Radicals - Chapter 9 Review Problem Set - Page 430: 54

$\dfrac{16\sqrt{10}}{5}$

Using the properties of radicals, the given expression, $ 3\sqrt{10}+\sqrt{\dfrac{2}{5}} ,$ simplifies to \begin{array}{l}\require{cancel} 3\sqrt{10}+\sqrt{\dfrac{2}{5}\cdot\dfrac{5}{5}} \\\\= 3\sqrt{10}+\sqrt{\dfrac{10}{25}} \\\\= 3\sqrt{10}+\dfrac{\sqrt{10}}{\sqrt{25}} \\\\= 3\sqrt{10}+\dfrac{\sqrt{10}}{5} \\\\= \dfrac{15\sqrt{10}}{5}+\dfrac{\sqrt{10}}{5} \\\\= \dfrac{16\sqrt{10}}{5} .\end{array}