Conjugate (square roots)

This article is about binomial conjugates in algebra. For other uses, see Conjugate (disambiguation).

In algebra, a conjugate is a binomial formed by negating the second term of a binomial. The conjugate of x + y is x − y, where x and y are real numbers. If y is imaginary, the process is termed complex conjugation: the complex conjugate of a + bi is a − bi, where a and b are real.

Differences of squares

Main article: Difference of two squares

In a commutative ring, an expression of the form

$a^{2}-b^{2}$

can be factored to give

$(a+b)(a-b)$

where one factor is the conjugate of the other. This can be useful when trying to rationalize a denominator containing radicals.

See also

• Conjugate element (field theory)

External links

• Rationalizing the Denominator from Mathwords.com