Roots, Radicals, and Root Functions

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Presentation transcript:

Roots, Radicals, and Root Functions Chapter 9 Roots, Radicals, and Root Functions

Radical Expressions and Graphs 9.1 Radical Expressions and Graphs

9.1 Radical Expressions and Graphs Objectives Find roots of numbers. Find principal roots. Graph functions defined by radical expressions. Find nth roots of nth powers. Use a calculator to find roots. Copyright © 2010 Pearson Education, Inc. All rights reserved.

9.1 Radical Expressions and Graphs Find Roots of Numbers In Section 1.3, we found square roots of positive numbers such as and because 10 • 10 = 100 and 11 • 11 = 121. Copyright © 2010 Pearson Education, Inc. All rights reserved.

9.1 Radical Expressions and Graphs Find Roots of Numbers Simplifying Higher Roots Copyright © 2010 Pearson Education, Inc. All rights reserved.

9.1 Radical Expressions and Graphs Finding Principal Roots Copyright © 2010 Pearson Education, Inc. All rights reserved.

9.1 Radical Expressions and Graphs Finding Roots Because the radicand, 25, is positive, there are two square roots, –5 and 5. The principal root is 5. Here, we want the negative square root, –5. The index is even and the radicand is negative, so this is not a real number. The index is odd, so the root is –4 since (–4)3 = –64. Copyright © 2010 Pearson Education, Inc. All rights reserved.

9.1 Radical Expressions and Graphs Graphs of Functions Defined by Radical Expressions Copyright © 2010 Pearson Education, Inc. All rights reserved.

9.1 Radical Expressions and Graphs Graphs of Functions Defined by Radical Expressions Copyright © 2010 Pearson Education, Inc. All rights reserved.

9.1 Radical Expressions and Graphs Graphs of Functions Defined by Radical Expressions Copyright © 2010 Pearson Education, Inc. All rights reserved.

9.1 Radical Expressions and Graphs Simplifying Square Roots Using Absolute Value Copyright © 2010 Pearson Education, Inc. All rights reserved.

9.1 Radical Expressions and Graphs Simplifying Higher Roots Using Absolute Value Copyright © 2010 Pearson Education, Inc. All rights reserved.

9.1 Radical Expressions and Graphs Use a Calculator to Find Roots Examples: Copyright © 2010 Pearson Education, Inc. All rights reserved.

9.1 Radical Expressions and Graphs Using a Calculator to Find the Velocity of an Orbiting Body Copyright © 2010 Pearson Education, Inc. All rights reserved.