Chapter 9 Section 4 Dividing Square Roots

Learning Objective 1.Understand what it means for a square root to be simplified 2.Use the Quotient Rule to simplify square roots 3.Rationalize denominators 4.Rationalize a denominator that contains a binomial

Key Vocabulary simplified square roots quotient rule for square roots rationalizing a denominator conjugate of a binominal

Simplifying Square Roots Simplified Square Roots have 1.No radicand has a factor that is a perfect square 2.No radicand contains a fraction 3.No denominator contains a square root

Rule # 3 – Quotient Rule for Square Roots When square roots contain a fraction divide out the common factors, then use the quotient rule to simplify Example: Quotient Rule for Square Roots

Example: Simplify Square Roots Using Quotient Rule

Example: Simplify Square Roots Using Quotient Rule

Example: Simplify Square Roots Using Quotient Rule

Rationalizing the denominator means to remove all radicals from the denominator. To rationalize a denominator with a square root: Multiply both the numerator and the denominator of the fraction by the square root that appears in denominator or by the square root of a number that makes the denominator a perfect square Example: Rationalize Denominators

Example: Rationalize Denominators

Conjugate is a binomial having the same two terms with the sign of the second term changed. BinomialConjugate Multiply both the numerator and denominator by the conjugate of the denominator. When multiplied using FOIL the sum of the Outer and Inner terms is 0 Rationalize Denominators that contain Binomials

Example: Rationalize Denominators that contain Binomials

Example: Rationalize Denominators that contain Binomials

Remember Rule # 1 - Product Rule for Square Roots Rule #2: Square Root of a Perfect Square The square root of a variable raised to an even power equals the variable raised to ½ that power. Rule # 3 – Quotient Rule for Square Roots

HOMEWORK 9.4 Page : # 13, 15, 19, 23, 31, 37, 41, 43, 61, 71