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Conjugate
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
In Algebra 1, the term "conjugate" typically refers to a pair of binomials involving square roots. When you have an expression like a + sqrt(b), its conjugate is a - sqrt(b), and vice versa.
For example:
The conjugate of 3 + sqrt(5) is 3 - sqrt(5).
The conjugate of 2 - sqrt(7) is 2 + sqrt(7).
Conjugates are often used to simplify expressions, especially when multiplying binomials with square roots. When you multiply a binomial by its conjugate, the result is a difference of squares, which eliminates the square root.
For example:
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