# How do you rationalize the denominator: 3/sqrt3?

Mar 7, 2018

$\sqrt{3}$

#### Explanation:

This means that you do not want an irrational number (surd) in the denominator

$\frac{3}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} \text{ } \leftarrow \frac{\sqrt{3}}{\sqrt{3}} = 1$

$= \frac{3 \sqrt{3}}{{\sqrt{3}}^{2}}$

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

$= \sqrt{3}$

Mar 7, 2018

3/sqrt3=color(blue)((3sqrt3)/3

#### Explanation:

Given:

$\sqrt{3}$

Rationalize the denominator by multiplying the numerator and denominator by $\sqrt{3}$.

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

Apply the rule $\sqrt{a} \sqrt{a} = a$.

$\frac{3 \sqrt{3}}{3}$

Simplify.

$\frac{{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}}^{1} \sqrt{3}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}} ^ 1$

$\sqrt{3}$ $\leftarrow$ answer