Chapter 7 - Section 7.4 - Adding, Subtracting, and Multiplying Radical Expressions - Exercise Set - Page 438: 15

$\dfrac{5\sqrt[]{5x}}{9}$

Using the properties of radicals, then, \begin{array}{l} \dfrac{\sqrt[]{20x}}{9}+\sqrt[]{\dfrac{5x}{9}} \\\\= \dfrac{\sqrt[]{4\cdot5x}}{9}+\dfrac{\sqrt{5x}}{3} \\\\= \dfrac{2\sqrt[]{5x}}{9}+\dfrac{\sqrt{5x}}{3} \\\\= \dfrac{2\sqrt[]{5x}+3\sqrt{5x}}{9} \\\\= \dfrac{5\sqrt[]{5x}}{9} .\end{array}