How do you simplify 2/sqrt7?

Jan 24, 2017

Multiply numerator and denominator by $\sqrt{7}$:

Explanation:

$\frac{2}{\sqrt{7}} \cdot \left(\frac{\sqrt{7}}{\sqrt{7}}\right)$ = $\frac{2 \sqrt{7}}{7}$.
That is considered "rationalized" since the denominator is now a rational number, 7.

Example: Simplify $\frac{2}{3 \sqrt{12}}$

Simplify the denominator first, then rationalize.
$\frac{2}{3 \sqrt{4} \sqrt{3}}$=$\frac{2}{3 \cdot 2 \sqrt{3}}$= $\frac{2}{6 \sqrt{3}}$

and reduce the $\frac{2}{6}$ = $\frac{1}{3 \sqrt{3}}$.

NOW, multiply top and bottom by $\sqrt{3}$:

$\frac{1}{3 \sqrt{3}} \cdot \left(\frac{\sqrt{3}}{\sqrt{3}}\right)$ = $\frac{\sqrt{3}}{3 \cdot 3}$= $\frac{\sqrt{3}}{9}$.