Chapter 7 - Section 7.5 - Multiplying with More Than One Term and Rationalizing Denominators - Exercise Set - Page 551: 105

$ \displaystyle \frac{3\sqrt{2}}{2}$

Rationalize $\displaystyle \frac{1}{\sqrt{2}}$ $\displaystyle \frac{1}{\sqrt{2}} \color{red}{ \cdot\frac{\sqrt{2}}{\sqrt{2}} }=\frac{\sqrt{2}}{2}$ $\displaystyle \sqrt{2}+ \frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{1}+\frac{\sqrt{2}}{2}=\frac{2\cdot\sqrt{2}+\sqrt{2}}{2}$ $=\displaystyle \frac{3\sqrt{2}}{2}$