1. Drill #63 Find the following roots: Factor the following polynomial:

2. Drill #64 Find the following roots:

3. Drill #65 Find the following roots:

4. Drill #66 Simplify each expression:

5. Drill #70 Simplify each expression:

6. 5-6 Radical Expressions Objective: To simplify radical expressions, to rationalize the denominator of radical expressions, and to add, subtract, multiply and divide radical expressions.

7. (1.) Product Property of Radicals ** Definition: For any real numbers a and b, and any integer n, n > 1, Example:

8. Examples/Classwork* Example: Example 1 (5-6 Study Guide) 5-6 Study Guide #1 – 3

9. (2.) Quotient Property of Radicals ** Definition: For real numbers a and b, b = 0, and any integer n, n > 1, Example:

10. Simplifying Radical Expressions: Using the Product Property Simplify the following:

11. Examples: 5-6 Skills Practice #5,6

12. Simplifying Radical Expressions: Using the Quotient Property Simplify the following:

13. (3.)Rationalizing the Denominator ** Definition: To rationalize the denominator you must multiply the numerator and denominator by a quantity so that the radicand (what’s inside the radical) has an exact root. We rationalize the denominator so that there are no radicals in denominator.

14. Rationalizing the Denominator* Example: 5-6 Study Guide

15. (4.) Like Radical Expressions Definition: Two radical expressions that have the same indices and the same radicand. To simplify like radical expressions add (or subtract) the coefficients. Examples:

16. Like Radical Expressions Group together all like radical expressions

17. Like Radical Expressions Group together all like radical expressions

18. Adding and Subtracting Radical Expressions* To add and subtract radical expressions: 1. Simplify all radicals in the expression to simplest form 2. Group together all like terms (non-radicals and radicals) 3. Add/subtract like terms to simplify Example:

19. Adding and Subtracting Radical Expressions* To add and subtract radical expressions: 1. Simplify all radicals in the expression to simplest form 2. Group together all like terms (non-radicals and radicals) 3. Add/subtract like terms to simplify Example:

20. Adding and Subtracting Radical Expression* To add and subtract radical expressions: 1. Simplify all radicals in the expression to simplest form 2. Group together all like terms (non-radicals and radicals) 3. Add/subtract like terms to simplify Example:

21. Multiplying Radical Expressions* To multiply radical expressions: 1. Use the distributive property (or FOIL) to multiply 2. Use the product property to multiply radicals. 3. Simplify each radical expression. 4. Combine like terms Example:

22. Multiplying Radical Expressions* Examples:

23. (5.) Conjugates** Definition: The conjugate of a radical expression is formed by changing the sign of the operation that joins the terms. Radical ExpressionConjugate

24. Multiplying conjugates What happens when you multiply conjugates?

25. Rationalize Radical Denominators* To rationalize radical denominators, multiply the numerator and the denominator by the conjugate of the denominator.

26. Rationalize Denominators* Examples: 5-6 Study Guide, Example 3

27. Drill #70 (Multiply Radicals) Simplify each expression:

28. Drill #70 (Divide Radicals) Simplify each expression:

29. Drill #70 (Add Radicals) Simplify each expression:

30. Drill #70 (Multiply Complex Radicals) Simplify each expression:

31. Drill #70 (Divide Complex Radicals) Simplify each expression:

32. Drill #70 (Divide Complex Radicals) Simplify each expression: