### Home > PC3 > Chapter 1 > Lesson 1.2.1 > Problem1-72

1-72.

In this course, you will need to rationalize the denominator (make the denominator a rational number) of fractions with radicals in the denominator. Before calculators, there was good reason to rationalize denominators—all calculations had to be done by hand. Consider dividing $1$ by $\sqrt { 3 }$, or $\frac { 1 } { \sqrt { 3 } }$. What about dividing $\sqrt { 3 }$ by $3$, or $\frac { \sqrt { 3 } } { 3 }$? Since $\frac { \sqrt { 3 } } { 3 }$ was a more useful form, it became the standard form. Use the following method to rationalize the denominator of each radical expression below: $\frac{1}{\sqrt{3}}·\frac{\sqrt{3}}{\sqrt{3}}=\frac{\sqrt{3}}{3}$

1. $\frac { 2 } { \sqrt { 3 } }$

This is the same as the example, but with a numerator of $2$.

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

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

1. $\frac { 2 } { 3 \sqrt { 5 } }$

$\frac{2}{3\sqrt{5}}\cdot\frac{\sqrt{5}}{\sqrt{5}}$