Radical Expressions and Graphs

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Sharp Tutor Mon, Jan 17, 2022 07:09 PM UTC

OBJECTIVE:
1. Find roots of numbers. 2. Find principal roots. 3. Graph functions defined by radical expressions. 4. Find nth roots of nth powers. 5. Use a calculator to find roots.

1. Copyright © 2010 Pearson Education, Inc. All rights reserved
Sec 9.1 - 1

2. Chapter 9
Roots, Radicals, and Root
Functions
Copyright © 2010 Pearson Education, Inc. All rights reserved
Sec 9.1 - 2

3. 9.1
Radical Expressions and
Graphs
Copyright © 2010 Pearson Education, Inc. All rights reserved
Sec 9.1 - 3

4. 9.1 Radical Expressions and Graphs
Objectives
1. Find roots of numbers.
2. Find principal roots.
3. Graph functions defined by radical
expressions.
4. Find nth roots of nth powers.
5. Use a calculator to find roots.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.1 - 4

5. 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. Sec 9.1 - 5

6. 9.1 Radical Expressions and Graphs
Find Roots of Numbers
Simplifying Higher Roots
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.1 - 6

7. 9.1 Radical Expressions and Graphs
Finding Principal Roots
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.1 - 7

8. 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. Sec 9.1 - 8

9. 9.1 Radical Expressions and Graphs
Graphs of Functions Defined by Radical Expressions
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.1 - 9

10. 9.1 Radical Expressions and Graphs
Graphs of Functions Defined by Radical Expressions
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.1 - 10

15. 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. Sec 9.1 - 15

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