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Conjugates

Now we will work with special pairs of binomial radical expression such as the following:

Notice that in each binomial pair, the first terms are the same and the second terms differ only in sign.

Such pairs of binomial radical expressions are called conjugates.

 

Definition — Conjugates

Two binomial radical expressions of the form are called conjugates.

Here, a, b, c, and d are rational numbers. Also, and are not both rational.

The product of conjugates is a rational number.

 

Example 1

Find:

Solution
Use the FOIL method.
Multiply.
The two middle terms are opposites and add to zero. = 10 - 9· 2
Simplify. = 10 - 18

= -8

Thus,
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