# How do you simplify sqrt3/-sqrt21?

Oct 12, 2015

$- \frac{\sqrt{7}}{7}$

#### Explanation:

The firs thing to notice here is that you can write $21$ as

$21 = 7 \cdot 3$

This means that the denominator of the fraction will be equivalent to

$\sqrt{21} = \sqrt{3 \cdot 7} = \sqrt{3} \cdot \sqrt{7}$

SInce $\sqrt{3}$ is present in both the numerator, and the denominator of the fraction, it will cancel out to give

$\frac{\sqrt{3}}{- \sqrt{21}} = - \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{\sqrt{3}}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{\sqrt{3}}}} \cdot \sqrt{7}} = - \frac{1}{\sqrt{7}}$

Next, rationalize the denominator by multiplying the fraction by $1 = \frac{\sqrt{7}}{\sqrt{7}}$

$- \frac{1}{\sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}} = - \frac{\sqrt{7}}{\sqrt{7} \cdot \sqrt{7}} = - \frac{\sqrt{7}}{\sqrt{7 \cdot 7}} = \textcolor{g r e e n}{- \frac{\sqrt{7}}{7}}$