If you've ever felt that math unfairly discriminates against negative square roots, this topic is for you. If a and b are rational numbers, the conjugate of a + b√d is a - b√d, even if a is zero. For example, the conjugate of 0 + √3 is 0 - √3, the conjugate of -√3 is √3, and the conjugate of 2 - 5√3 is 2 + 5√3.