# How do you rationalize the denominator and simplify sqrt(14/3)?

Feb 27, 2017

$\sqrt{\frac{14}{3}} = \frac{\sqrt{42}}{3}$

#### Explanation:

$\sqrt{\frac{14}{3}} = \frac{\sqrt{14}}{\sqrt{3}}$

color(white)("XXX")=sqrt(14)/sqrt(3) xx sqrt(3)/(sqrt(3)

$\textcolor{w h i t e}{\text{XXX}} = \frac{\sqrt{14 \times 3}}{3}$

$\textcolor{w h i t e}{\text{XXX}} = \frac{\sqrt{42}}{3}$

(note: $42$ has no square integer factors and can not be simplified any further)