1. Copyright © 2015, 2011, 2007 Pearson Education, Inc. 1 1 Chapter 8 Rational Exponents, Radicals, and Complex Numbers

2. Copyright © 2015, 2011, 2007 Pearson Education, Inc. 2 Rational Exponents, Radicals, and Complex Numbers 8.1Radical Expressions and Functions 8.2Rational Exponents 8.3Multiplying, Dividing, and Simplifying Radicals 8.4Adding, Subtracting, and Multiplying Radical Expressions 8.5Rationalizing Numerators and Denominators of Radical Expressions 8.6Radical Equations and Problem Solving 8.7Complex Numbers CHAPTER 8

3. Copyright © 2015, 2011, 2007 Pearson Education, Inc. 3 Adding, Subtracting, and Multiplying Radical Expressions 1.Add or subtract like radicals. 2.Use the distributive property in expressions containing radicals. 3.Simplify radical expressions that contain mixed operations. 8.4

4. Copyright © 2015, 2011, 2007 Pearson Education, Inc. 4 Like radicals: Radical expressions with identical radicands and identical root indices. Adding Like Radicals To add or subtract like radicals, add or subtract the coefficients and leave the radical parts the same.

5. Copyright © 2015, 2011, 2007 Pearson Education, Inc. 5 Example Add or subtract. a. b. Solution a. b.

6. Copyright © 2015, 2011, 2007 Pearson Education, Inc. 6 continued Simplify. c. d. Solution c. d. Combine the like radicals by subtracting the coefficients and keeping the radical. Regroup the terms.

7. Copyright © 2015, 2011, 2007 Pearson Education, Inc. 7 Example Add or subtract. a. b. Solution a. b. Factor 28. Combine like radicals. Simplify.

8. Copyright © 2015, 2011, 2007 Pearson Education, Inc. 8 continued c. Solution c.

9. Copyright © 2015, 2011, 2007 Pearson Education, Inc. 9 Example Find the product. Solution Use the distributive property. Multiply.

10. Copyright © 2015, 2011, 2007 Pearson Education, Inc. 10 Example Find the product. Solution Use the product rule. Use the distributive property. Find the products. Combine like radicals.

11. Copyright © 2015, 2011, 2007 Pearson Education, Inc. 11 Example Find the product. Solution

12. Copyright © 2015, 2011, 2007 Pearson Education, Inc. 12 Example Find the product. Solution Simplify. Use (a – b) 2 = a 2 – 2ab – b 2.

13. Copyright © 2015, 2011, 2007 Pearson Education, Inc. 13 Example Find the product. Solution Simplify. Use (a + b)(a – b) = a 2 – b 2.

14. Copyright © 2015, 2011, 2007 Pearson Education, Inc. 14 Example Find the product. Solution

15. Copyright © 2015, 2011, 2007 Pearson Education, Inc. 15 Example Simplify. a. Solution a. b.