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 Depdendent Variable

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 Dependent Variable

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# 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