In this Section:
In this section, we continue to learn about the simplified form of a radical. We will take all of the knowledge that we have learned so far, and look at some more complicated scenarios. These problems will involve: multiplication, multiplication with FOIL, utilizing special products formulas, and division. We will also encounter the problem of trying to rationalize a denominator with two terms, where at least one of the terms is a radical. In order to do this, we must first understand the concept of a conjugate. A conjugate occurs when we have two terms, keep them the same, but we change the sign. For example, 3n - 7 and 3n + 7 are conjugates. The terms in the first position are the same along with the terms in the second position. The only difference is the sign. We will use conjugates to rationalize a denominator with two terms, where at least one is a radical.