# How do you simplify: square root of 1/3?

Jul 24, 2015

Usually the final answer is written as $\frac{\sqrt{3}}{3}$

#### Explanation:

To get the final answer, you need to "rationalize the denominator" by multiplying by $1 = \frac{\sqrt{3}}{\sqrt{3}}$ as follows:

$\sqrt{\frac{1}{3}} = \frac{\sqrt{1}}{\sqrt{3}} = \frac{1}{\sqrt{3}} = \frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{3}}{3}$

It is not "mathematically illegal" to write this number as $\frac{1}{\sqrt{3}}$ (it's not like dividing by zero or something), but the standard convention is to avoid roots in denominators, if possible. This is done for two main reasons: