Chapter 7 - Section 7.4 - Adding, Subtracting, and Multiplying Radical Expressions - Exercise Set - Page 438: 11

$\dfrac{26\sqrt{2}}{15}$

Using the properties of radicals, then, \begin{array}{l} \dfrac{4\sqrt{2}}{3}+\dfrac{2\sqrt{2}}{5} \\\\= \dfrac{5(4\sqrt{2})+3(2\sqrt{2})}{15} \\\\= \dfrac{20\sqrt{2}+6\sqrt{2}}{15} \\\\= \dfrac{26\sqrt{2}}{15} .\end{array}