Rationalizing a Binomial Denominator

In this section, we will learn how to rationalize a binomial denominator (two terms) along with how to rationalize any denominator that is more than one single term. When we encounter a binomial denominator with a radical involved, we can’t simply multiply the numerator and denominator by the radical. We begin by learning about the conjugate. The conjugate is obtained by keeping the terms the same and changing the sign between the two. Once we have obtained the conjugate, we can use this to rationalize a binomial denominator. We will multiply the numerator and denominator by the conjugate. This creates a scenario in the denominator that turns into the difference of two squares, once the multiplication is done. We will then move into a more advanced scenario, rationalizing a trinomial denominator. For us to rationalize a denominator with more than two terms, we rely on a grouping trick.