# How do you simplify sqrt(14)/sqrt(21)?

Oct 1, 2015

Note that $14 = 2 \cdot 7 \mathmr{and} 21 = 3 \cdot 7$

#### Explanation:

We can now rewrite:

$\sqrt{14} = \sqrt{2 \cdot 7} = \sqrt{2} \cdot \sqrt{7}$, and:
$\sqrt{21} = \sqrt{3 \cdot 7} = \sqrt{3} \cdot \sqrt{7}$

Putting this together, we get:

$= \frac{\sqrt{2} \cdot \cancel{\sqrt{7}}}{\sqrt{3} \cdot \cancel{\sqrt{7}}} = \frac{\sqrt{2}}{\sqrt{3}}$

If you multiply both halves of the fraction by $\sqrt{3}$:

$= \frac{\sqrt{3} \cdot \sqrt{2}}{\sqrt{3} \cdot \sqrt{3}} = \frac{\sqrt{6}}{3} = \frac{1}{3} \sqrt{6}$