1. Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 9.3 - 1

2. Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 9.3 - 2 Roots, Radicals, and Root Functions Chapter 9

3. Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 9.3 - 3 9.3 Simplifying Radical Expressions

4. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.3 - 4 9.3 Radical Expressions and Graphs Objectives 1.Use the product rule for radicals. 2.Use the quotient rule for radicals. 3.Simplify radicals. 4.Simplify products and quotients of radicals with different indexes. 5.Use the Pythagorean formula. 6.Use the distance formula.

5. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.3 - 5 9.3 Simplifying Radical Expressions Use the Product Rule for Radicals

6. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.3 - 6 9.3 Simplifying Radical Expressions Use the Product Rule for Radicals Cannot be simplified using the product rule because the indexes, are different.

7. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.3 - 7 9.3 Simplifying Radical Expressions Use the Quotient Rule for Radicals

8. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.3 - 8 9.3 Simplifying Radical Expressions Simplifying Radicals

9. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.3 - 9 9.3 Simplifying Radical Expressions Simplifying Radicals Cannot be simplified further. Be careful to leave the 5 inside the radical.

10. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.3 - 10 9.3 Simplifying Radical Expressions Simplifying Radicals with Variables Assume all variables represent positive real numbers.

11. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.3 - 11 9.3 Simplifying Radical Expressions Simplifying Radicals with Variables Assume all variables represent positive real numbers.

12. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.3 - 12 9.3 Simplifying Radical Expressions Simplifying Radicals – Smaller / Different Indices Assume all variables represent positive real numbers.

13. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.3 - 13 9.3 Simplifying Radical Expressions Pythagorean Formula The Pythagorean formula relates lengths of the sides of a right triangle.

14. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.3 - 14 9.3 Simplifying Radical Expressions Pythagorean Formula 90 º a 9 5

15. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.3 - 15 9.3 Simplifying Radical Expressions The Distance Formula The distance formula, which allows us to compute the distance between two points in the coordinate plane is derived from the Pythagorean formula. Find the distance between (1, 6) and (4, –2).

16. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.3 - 16 9.3 Simplifying Radical Expressions The Distance Formula This is the same answer we obtained using the Pythagorean formula.