# How do you simplify 3/sqrt3?

Since $\frac{3}{\sqrt{3}}$ has a radical in its denominator, you must do a process known as rationalization. Rationalization is when you must multiply the whole fraction by another fraction where the numerator and denominator are $\sqrt{3}$. By doing so, you remove the radical, since $\sqrt{3}$ $\left(1.7320508 \ldots\right)$ is irrational, that is, the decimal goes on forever without repeating.
$\frac{3}{\sqrt{3}} \textcolor{red}{\cdot \frac{\sqrt{3}}{\sqrt{3}}}$
$= \frac{3 \textcolor{red}{\cdot \sqrt{3}}}{\sqrt{3} \textcolor{red}{\cdot \sqrt{3}}}$
$= \frac{3 \sqrt{3}}{3}$
Notice how once you rationalize the fraction, the denominator is not irrational anymore. Also, keep in mind that you did not change the value of the simplified fraction. Since $\frac{\sqrt{3}}{\sqrt{3}}$ is equal to $1$, you simply rearranged the way it was written. The value of the simplified fraction stays the same.