Conjugate of Denominator SIMPLIFYING QUOTIENTS OF RADICALS 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. _NUMERATOR_ DENOMINATOR Conjugate of Denominator _NUMERATOR_ DENOMINATOR Example 1 Rationalizing Square Roots [B] [A]

Practice Rationalizing Square Roots [2] [1] [3] [4]

Example 2 Rationalizing Square Roots with variables When using variables, how many more variables are needed to complete the index. Square roots = make pairs with all variables. [B] [A] [C] [d]

Example 3: Rationalizing Cube Roots [D] [C]

PRACTICE: Rationalizing Cube Roots [2] [1] [4] [3]

Example 4 Tougher Rationalizing – Multiple Variables [C] [D]

PRACTICE - Simplifying Radicals: [1] [2] [3] [4] [5] [6]

PRACTICE - Simplifying Radicals: continued [7] [8] [9] [12] [10] [11]

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

What is the Binomial Conjugate and Find the product? [1] [2] [3] [4]

Example 1: Use Binomials Conjugates to Rationalize

Practice: Use Binomials Conjugates to Rationalize [1] [2] [3] [4]