### Home > PC3 > Chapter 1 > Lesson 1.2.3 > Problem1-101

1-101.

Rationalizing the denominator can make it easier to recognize “like terms” in expressions.
For example, $\sqrt { 2 }$ and $\frac { 1 } { \sqrt { 2 } }$ can be combined if $\frac { 1 } { \sqrt { 2 } }$ is rewritten as $\frac { 1 } { \sqrt { 2 } } \cdot \frac { \sqrt { 2 } } { \sqrt { 2 } } = \frac { \sqrt { 2 } } { 2 }$.
Then $\sqrt { 2 } + \frac { 1 } { \sqrt { 2 } } = \sqrt { 2 } + \frac { \sqrt { 2 } } { 2 } = \frac { 3 \sqrt { 2 } } { 2 }$.
Use this method to combine the like terms of each radical expression below.

1. $8\sqrt { 2 }-\frac{8}{\sqrt{2}}$

$8\sqrt{2}-\frac{8}{\sqrt{2}}\cdot\frac{\sqrt{2}}{\sqrt{2}}$

$8\sqrt{2}-4\sqrt{2}$

1. $-5\sqrt{6}+\frac{4}{\sqrt{6}}$

$-5\sqrt{6}+\frac{4}{\sqrt{6}}\cdot\frac{\sqrt{6}}{\sqrt{6}}$

$-5\sqrt{6}+\frac{2}{3}\sqrt{6}$

$-\frac{15}{3}\sqrt{6}+\frac{2}{3}\sqrt{6}$