How to Factor Square Roots in a Denominator
- 1). Simplify the denominator's fraction by extracting the square root if the number under the radical is a perfect square. For example, if you have 5/√25, 25 is a perfect square that can be simplified to 5. The fraction would then be 5/5, which equals 1.
- 2). Multiply the top (numerator) and bottom (denominator) of the fraction by the term in the denominator if you do not have a perfect square in the denominator. For instance if you have 2/√3, you would multiply the top and bottom by √3 to get 2√3/√3(√3).
- 3). Remove the radical in the denominator. In this example, you can see that √3 times √3 equals √9. Because the square root of 9 is 3, the shortcut to this process is simply to remove the radical sign from √3. Your answer would then be 2√3/3.
- 4). Multiply the numerator and the denominator by any square root that may be left in the denominator after extracting any perfect squares. This will get rid of the square root in the denominator. For instance, if you have 1/√72, you would simplify √72 to √36 * √2, which equals 6√2. Then you would multiply the numerator and denominator by √2 to get a final answer of √2/12.
Source...