In my precalc 11 class this week, I learned how to rationalize a denominator. This happens when there is a fraction with a square root on the bottom. For example:
When fractions are being simplified, it is better to show them with an integer on the bottom. If the denominator is not an integer, but a radical, you can rationalize it. To make the denominator a rational number, or a non-radical, multiply the whole fraction by 1. This is done my multiplying it by the radical on the bottom, that you want to get rid of. (Since the radical is on the top and bottom of a fraction it equals 1).
These fractions below are all equal to 1, because the numerator and denominator are the same:
When you multiply the two fractions, make sure to multiply the radicals only with other radicals, and integers in front of the radicals (if it’s a mixed radical) with other integers. If there is no number in front of a radical, pretend there is a 1. Make sure not to multiply a radical with an integer! Here are a few examples of how to rationalize the denominator: