# How do you rationalize (3sqrt7)/12?

May 15, 2015

The expression $\frac{3 \sqrt{7}}{12}$ can not be rationalized.

Any attempt to remove the radical from the numerator would cause a radical to appear in the denominator.

For example
$\frac{3 \sqrt{7}}{12} \cdot \frac{\sqrt{7}}{\sqrt{7}}$

$\frac{3 \cdot 7}{12 \cdot \sqrt{7}} = \frac{21}{12 \sqrt{7}}$
...and we're still stuck with a radical.

The most that can be done is simplification:
$\frac{3 \sqrt{7}}{12} = \frac{\sqrt{7}}{4}$