1. Chapter 9 Section 2 Simplifying Square Roots

2. Learning Objective 1.Use the product rule to simplify square roots containing constants 2.Use the product rule to simplify square roots containing variables

3. Key Vocabulary product rule for square roots perfect square perfect square factor

4. Product Rule to Simplify Square Roots Containing Constants Rule # 1 - Product Rule for Square Roots Example: All are factors of

5. Simplify Square Roots Containing Constants 1.Write the constant as a product of the largest perfect square and another factor 2.Use the Product Rule to write the expression as a product of square roots, with each square roots containing one of the factors 3.Find the square root of the perfect square factor

6. Product Rule to Simplify Square Roots Containing Constants Examples:

7. Product Rule to Simplify Square Roots Containing Constants Examples:

8. Product Rule to Simplify Square Roots Containing Constants Examples:

9. Product Rule to Simplify Square Roots Containing Constants When working with large radicand may have to continue to simplify Examples:

10. Square Roots of a Perfect Square Perfect squares can also be variables when raised to an even exponent Examples: 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.

11. Square Roots of Even Power Examples:

12. Square Roots of Odd Power To simplify the Square Root of a Radicand Containing a Variable Raised to an Odd Power 1.Express the variable as the product of two factors, one being to the first power this makes the other a perfect square 2.Use the product rule to simplify

13. Square Roots of Odd Power Exp.

14. Square Roots of Odd Power Exp:

15. Square Roots of Odd Power Exp.

16. Remember Rule # 1 - Product Rule Even Powers - The square root of a variable raised to an even power equals the variable raised to ½ that power. Odd Powers - Express the variable as the product of two factors, one being to the first power this makes the other a perfect square then use the product rule to simplify.

17. Remember Even though we are assuming all variables represent nonnegative real numbers, remember that When simplifying radicals, we sometimes forget to pull numbers outside the radical symbol.

18. HOMEWORK 9.2 Page 545 - 546: #15, 25, 27, 31, 33, 35, 39, 47, 55, 57, 65