# How do you rationalize the denominator and simplify (6sqrt3)/sqrt14?

Jul 26, 2016

$6 \frac{\sqrt{3}}{\sqrt{14}} = \textcolor{g r e e n}{\frac{3}{7} \sqrt{42}}$
Multiplying the numerator and denominator by $\sqrt{14}$
$\frac{6 \sqrt{3}}{\sqrt{14}} \times \frac{\sqrt{14}}{\sqrt{14}} = \frac{6 \sqrt{42}}{14} = \frac{3 \sqrt{42}}{7}$
Note that since $42$ contains no squared factors $\sqrt{42}$ can not be simplified.