Conjugates and Dividing by Square Roots
Students learn to get rid of a radical in the denominator of a fraction when there are two separate terms in the denominator, by multiplying both the numerator and denominator of the fraction by the conjugate of the denominator. The conjugate of an expression is identical to the original expression, except that the sign between the terms is changed. For example, the conjugate of (4 - 2 root 3) is (4 + 2 root 3). So to simplify 4/(4 - 2 root 3), multiply both the numerator and denominator by (4 + 2 root 3) to get rid of the radical in the denominator.