1. Chapter 9 Section 4 Dividing Square Roots

2. 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

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

4. 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

5. 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

6. Example: Simplify Square Roots Using Quotient Rule

7. Example: Simplify Square Roots Using Quotient Rule

8. Example: Simplify Square Roots Using Quotient Rule

9. 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

10. Example: Rationalize Denominators

11. 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

12. Example: Rationalize Denominators that contain Binomials

13. Example: Rationalize Denominators that contain Binomials

14. 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

15. HOMEWORK 9.4 Page 559 - 560: # 13, 15, 19, 23, 31, 37, 41, 43, 61, 71