# What is 3/sqrt3?

Sep 28, 2015

It's the same as $\sqrt{3}$.

#### Explanation:

There are a few different ways this can be seen.

1) Rationalize the denominator:

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

2) Use properties of exponents:

$\frac{3}{\sqrt{3}} = {3}^{1} / {3}^{\frac{1}{2}} = {3}^{1 - \frac{1}{2}} = {3}^{\frac{1}{2}} = \sqrt{3}$

3) Square it:

${\left(\frac{3}{\sqrt{3}}\right)}^{2} = \frac{{3}^{2}}{{\sqrt{3}}^{2}} = \frac{9}{3} = 3$, hence $\frac{3}{\sqrt{3}} = \sqrt{3}$.