1. Copyright © 2011 Pearson Education, Inc. Radical Functions Chapter 13

2. Copyright © 2011 Pearson Education, Inc. Simplifying Radical Expressions Section 13.1

3. Lehmann, Elementary and Intermediate Algebra, 1edSection 13.1Slide 3 Copyright © 2011 Pearson Education, Inc. Examples of radicals: Examples of radical expressions: Radical Expressions Definitions Definition

4. Lehmann, Elementary and Intermediate Algebra, 1edSection 13.1Slide 4 Copyright © 2011 Pearson Education, Inc. Evaluate the radical. Verify using a graphing calculator: Radical Expressions Evaluating Radicals Example Solution

5. Lehmann, Elementary and Intermediate Algebra, 1edSection 13.1Slide 5 Copyright © 2011 Pearson Education, Inc. If the expression is in exponential form, write it in radical form. If it is in radical form, write it in exponential form. Radical Expressions Writing Exponential and Radical Forms Example Solution

6. Lehmann, Elementary and Intermediate Algebra, 1edSection 13.1Slide 6 Copyright © 2011 Pearson Education, Inc. nth powers for n = 2, n = 3, and n =4: Radical Expressions Simplify Radical Expressions Property

7. Lehmann, Elementary and Intermediate Algebra, 1edSection 13.1Slide 7 Copyright © 2011 Pearson Education, Inc. If and are defined, then In words: The nth root of a product is the product of the nth roots. Radical Expressions Product Property for Radicals Property Proof

8. Lehmann, Elementary and Intermediate Algebra, 1edSection 13.1Slide 8 Copyright © 2011 Pearson Education, Inc. Simplify. Assume that x is nonnegative. Radical Expressions Simplifying Radical Expressions Example Solution

9. Lehmann, Elementary and Intermediate Algebra, 1edSection 13.1Slide 9 Copyright © 2011 Pearson Education, Inc. Radical Expressions Simplifying Radical Expressions ExampleSolution Continued

10. Lehmann, Elementary and Intermediate Algebra, 1edSection 13.1Slide 10 Copyright © 2011 Pearson Education, Inc. If the radicand has more than one numerical factor that is a perfect nth power, select the largest one If the radicand has more than one factor that is a perfect nth power with the same variable base, select the one with the largest exponent Simplify. Assume that all variables are nonnegative. Radical Expressions Simplifying Radical Expressions Guidelines Example

11. Lehmann, Elementary and Intermediate Algebra, 1edSection 13.1Slide 11 Copyright © 2011 Pearson Education, Inc. If the radicand has more than one numerical factor that is a perfect nth power, select the largest one. If the radicand has more than one factor that is a perfect nth power with the same variable base, select the one with the largest exponent. Simplify. Assume that all variables are nonnegative. Radical Expressions Simplifying Radical Expressions Solutions

12. Lehmann, Elementary and Intermediate Algebra, 1edSection 13.1Slide 12 Copyright © 2011 Pearson Education, Inc. Simplify. Assume that all variables are nonnegative. Radical Expressions Simplifying Radical Expressions Example Solution

13. Lehmann, Elementary and Intermediate Algebra, 1edSection 13.1Slide 13 Copyright © 2011 Pearson Education, Inc. Simplify. Assume that all variables are nonnegative. Radical Expressions Simplifying Radical Expressions ExampleSolution Continued

14. Lehmann, Elementary and Intermediate Algebra, 1edSection 13.1Slide 14 Copyright © 2011 Pearson Education, Inc. Simplify. Assume that x > 0. Radical Expressions Simplifying Radical Expressions Example Solution

15. Lehmann, Elementary and Intermediate Algebra, 1edSection 13.1Slide 15 Copyright © 2011 Pearson Education, Inc. Radical Expressions Simplifying Radical Expressions ExampleSolution Continued

16. Lehmann, Elementary and Intermediate Algebra, 1edSection 13.1Slide 16 Copyright © 2011 Pearson Education, Inc. Radical Expressions Simplifying Radical Expressions ExampleSolution Continued

17. Lehmann, Elementary and Intermediate Algebra, 1edSection 13.1Slide 17 Copyright © 2011 Pearson Education, Inc. Radical Expressions Simplifying Radical Expressions ExampleSolution Continued

18. Lehmann, Elementary and Intermediate Algebra, 1edSection 13.1Slide 18 Copyright © 2011 Pearson Education, Inc. Radical Expressions Simplifying a Radical Expressions Process To simplify a radical expression with index n, 1. Find perfect nth-power factors of the radicand. 2. Apply the product property for radicals. 3. Find the nth root of each perfect nth power. 4. Write the radical with as small an index as possible.

19. Lehmann, Elementary and Intermediate Algebra, 1edSection 13.1Slide 19 Copyright © 2011 Pearson Education, Inc. Radical Expressions Power Property for Radicals Property Let n be a counting number greater than 1: If n is even, then If n is odd, then

20. Lehmann, Elementary and Intermediate Algebra, 1edSection 13.1Slide 20 Copyright © 2011 Pearson Education, Inc. Radical Functions Evaluating Radical Functions Example For find the following: Solution

21. Lehmann, Elementary and Intermediate Algebra, 1edSection 13.1Slide 21 Copyright © 2011 Pearson Education, Inc. Radical Functions Evaluating Radical Functions Example Sketch a graph of Solution

22. Lehmann, Elementary and Intermediate Algebra, 1edSection 13.1Slide 22 Copyright © 2011 Pearson Education, Inc. Radical Functions Evaluating Radical Functions ExampleSolution Continued

23. Lehmann, Elementary and Intermediate Algebra, 1edSection 13.1Slide 23 Copyright © 2011 Pearson Education, Inc. Radical Mode Using a Square Rood Model to Make Predications Example The percentages of colleges and universities offering distance learning are shown in the table for various years. Let f (t) be the percentage of colleges and universities that offer distance learning at t years since 1997. A model of the situation is 1. Use a graphing calculator to draw the graph of f and, in the same viewing window, the scattergram of the data. Does the graph of f fit the data well?

24. Lehmann, Elementary and Intermediate Algebra, 1edSection 13.1Slide 24 Copyright © 2011 Pearson Education, Inc. 2. Predict the percentage of colleges and universities that will offer distance learning in 2007. Example Continued Radical Mode Using a Square Rood Model to Make Predications

25. Lehmann, Elementary and Intermediate Algebra, 1edSection 13.1Slide 25 Copyright © 2011 Pearson Education, Inc. 1.The graph of f and the scattergram of the data are shown in the figure. The model appears to fit the data well. 2.We evaluate f at 10: About 97.8% of colleges and universities will offer distance learning in 2007, according to the model. Radical Mode Using a Square Rood Model to Make Predications Solution