How do you rationalize $\frac{3 \sqrt{7}}{12}$ $(3sqrt7)/12$ ?

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Answer 1 · 2015-05-15T11:31:05

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

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

For example
$\frac{3 \sqrt{7}}{12} \cdot \frac{\sqrt{7}}{\sqrt{7}}$ $(3sqrt(7))/12* sqrt(7)/sqrt(7)$

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

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

How do you rationalize (3sqrt7)/123√712(3sqrt7)/12?