How do you find the square root of a fraction?

You take the square root of both the numerator and the denominator.

Thus the square root of 9/16 becomes 3/4.

The square root of a fraction is equal to the square root of the numerator divided by the square root of the denominator.

If your fraction is not written as a common fraction (for example, if it is a decimal fraction), you must first write it in that form. Then you find the square root by writing the square root of the numerator divided by the square root of the denominator. And, to write it properly, you then rationalise the resulting fraction, if the denominator ends up as a surd (see section 5 of the link). For example, the square root of 5/12 is (square root of 5) / 2 x (square root of 3). To remove the square root from the denominator, multiply both numerator and denominator by (square root of 3). This gives (square root of 15) / 6. If your final numerator and denominator have any common factors, the fraction should be simplified.

http://www.mathcentre.ac.uk/resources/workbooks/mathcentre/surds.pdf