Conjugates
In the previous example, we multiplied two radical expressions,
and
.
You may have been surprised that the result -22, does not contain a
radical.
Let’s recall why that is so.
We used the FOIL method to multiply:
![](./articles_imgs/310/conjug57.gif)
Let’s look again at the original two radical expressions.
![](./articles_imgs/310/conjug58.gif)
Such binomial radical expressions are called conjugates.
Here are some other examples of conjugates:
![](./articles_imgs/310/conjug59.gif)
When we multiply two conjugate radical expressions, the result is a
rational number. For this reason, conjugates are used to simplify certain
types of radical expressions.
Example 1
Multiply
by its conjugate.
Solution
The conjugate of
![](./articles_imgs/310/conjug61.gif) |
![](./articles_imgs/310/conjug62.gif) |
Use the FOIL method.
|
![](./articles_imgs/310/conjug63.gif) |
Multiply.
|
![](./articles_imgs/310/conjug64.gif) |
The two middle terms are
opposites and add to zero. |
![](./articles_imgs/310/conjug65.gif) |
Simplify
![](./articles_imgs/310/conjug66.gif) |
= 25 - 2 |
Subtract. |
= 23 |
|