How do you simplify 14/sqrt 11?

Feb 21, 2016

$\textcolor{b l u e}{\frac{14 \sqrt{11}}{11}}$

Explanation:

Since the given has an irrational deminator, Square Roots are not allowed in the denominator, we must rationalize the denominator.

$\frac{a}{\sqrt{b}} = \frac{a}{\sqrt{b}} \cdot \frac{\sqrt{b}}{\sqrt{b}} = \frac{a \sqrt{b}}{b}$

where $a > 0 , b > 0 , c > 0$

we can simply rationalize the denominator by simply multiplying the top and bottom by $\sqrt{11}$.
$\left(\frac{14}{\sqrt{11}}\right) \cdot \frac{\sqrt{11}}{\sqrt{11}} = \frac{14 \sqrt{11}}{11}$

So the answer is:

$\frac{14 \sqrt{11}}{11}$