1. Conjugate: Value or that is multiplied to a radical expression That clears the radical. Rationalizing: Removing a radical expression from the denominator of a fraction. Process: Multiply the fraction by a factor of one its conjugate of denominator. Example 1Rationalizing Square Roots [A] [B] SIMPLIFYING QUOTIENTS OF RADICALS _NUMERATOR_ DENOMINATOR Conjugate of Denominator _NUMERATOR_ DENOMINATOR

2. Example 2Rationalizing Square Roots Continued [A] [B]

3. Example 3Rationalizing Cube Roots [A] [B] [C] [D]

4. Example 4Tougher Rationalizing [A] [B]

5. [1][2][3][4] [5][6] [7][8] [9] [10] [11][12] PRACTICE - Simplifying Radicals: Use as separate paper.

6. Binomial Conjugate: Binomial that differ only by an addition or subtraction of terms. The product of binomial conjugates is a difference of squares (FOIL). [1] [2]

7. Example 1: Use Binomials Conjugates to Rationalize [A] [B]

8. Example 2: Use Binomials Conjugates to Rationalize [A][B]