This week in pre calc 11 I learned how to rationalize a denominator. This happens when there is a fraction with a square root on the bottom. For example:
When simplifying fractions, it’s best to present them with an integer at the bottom. You can rationalize the denominator if it is a radical rather than an integer. Multiply the full fraction by 1 to make the denominator a rational integer, or a non-radical. This is accomplished by multiplying it by the radical at the bottom of the equation that you want to eliminate. (The radical equals 1 since it is at the top and bottom of a fraction.)
These fractions below are all equal to 1, because the numerator and denominator are the same and have the same radicand.
Make sure you multiply the radicals with other radicals and the integers in front of the radicals (if it’s a mixed radical) with other integers when multiplying the two fractions. Pretend there’s a 1 in front of a radical if there isn’t one. Make sure you’re not multiplying a radical by a number! Here are some instances of denominator rationalization:
