# Conjugate (square roots)

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In mathematics, the **conjugate** of an expression of the form is provided that does not appear in a and b. One says also that the two expressions are conjugate. In particular, the conjugate of a root of a quadratic polynomial is the other root, obtained by changing the sign of the square root appearing in the quadratic formula.

Complex conjugation is the special case where the square root is

As

and

the sum and the product of conjugate expressions do not involve the square root anymore.

This property is used for removing a square root from a denominator, by multiplying the numerator and the denominator of a fraction by the conjugate of the denominator (see rationalisation). Typically, one has

In particular

## See also[edit]

- Conjugate element (field theory), the generalization to the roots of a polynomial of any degree