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.
Letâ€™s recall why that is so.
We used the FOIL method to multiply:
Letâ€™s look again at the original two radical expressions.
Such binomial radical expressions are called conjugates.
Here are some other examples of conjugates:
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


Use the FOIL method.


Multiply.


The two middle terms are
opposites and add to zero. 

Simplify

= 25  2 
Subtract. 
= 23 
