SIMPLIFYING QUOTIENTS OF RADICALS Conjugate Value or that

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_ Conjugate of Denominator _NUMERATOR_ DENOMINATOR Conjugate of Denominator Example 1 Rationalizing Square Roots [B] [A]

Practice [1] [3] Rationalizing Square Roots [2] [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. [A] [C] [B] [d]

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

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

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

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

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

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 [A] [B]

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