# What is the square root of the fraction 7/12?

Sep 12, 2015

$\sqrt{\frac{7}{12}} = \frac{\sqrt{21}}{6}$

#### Explanation:

$\sqrt{\frac{7}{12}} = \sqrt{\frac{21}{36}} = \frac{\sqrt{21}}{\sqrt{36}} = \frac{\sqrt{21}}{6}$

Why did I multiply both the numerator and denominator by $3$?

I noticed that $12 = {2}^{2} \cdot 3$ has one square factor in ${2}^{2} = 4$ and is only lacking another factor of $3$ to make a square number.

Then I used $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ allowing the resulting denominator to be an integer.