How do you rationalize the denominator and simplify sqrt21/sqrt6?

Mar 15, 2016

$\frac{\sqrt{106}}{6}$

Explanation:

$1$. Since the denominator of the fraction contains a radical, start by multiplying the numerator and denominator by $\frac{\sqrt{6}}{\sqrt{6}}$. Note that $\frac{\sqrt{6}}{\sqrt{6}} = 1$, so that value of the fraction remains the same.

$\frac{\sqrt{21}}{\sqrt{6}}$

$= \frac{\sqrt{21}}{\sqrt{6}} \left(\frac{\sqrt{6}}{\sqrt{6}}\right)$

$2$. Simplify.

$= \frac{\sqrt{21 \cdot 6}}{6}$

$= \textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \frac{\sqrt{106}}{6} \textcolor{w h i t e}{\frac{a}{a}} |}}}$