what if the denominator is negative, will the conjugate be positive? :D

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If the denominator is a - sqr(b) then the conjugate for clearing the radical from the denominator is a + sqr(b).  This is multiplied by top and bottom and is guaranteed to get rid of radicals in the denominator.  Just as a point of fact for the first reply, there are also conjugate acids and bases in chemistry, but these have nothing to do with the math problem.