Chapter 7 Roots Radicals and Root Functions Copyright

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Chapter 7 Roots, Radicals, and Root Functions Copyright © 2016, 2012, 2008 Pearson Education,

Chapter 7 Roots, Radicals, and Root Functions Copyright © 2016, 2012, 2008 Pearson Education, Inc. 1

Radical Expressions and Graphs 7. 1 1. 2. 3. 4. 5. Find roots of

Radical Expressions and Graphs 7. 1 1. 2. 3. 4. 5. 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 © 2016, 2012, 2008 Pearson Education, Inc. 2

Objective 1 Find roots of numbers. Copyright © 2016, 2012, 2008 Pearson Education, Inc.

Objective 1 Find roots of numbers. Copyright © 2016, 2012, 2008 Pearson Education, Inc. 3

Find roots of numbers. Copyright © 2016, 2012, 2008 Pearson Education, Inc. 4

Find roots of numbers. Copyright © 2016, 2012, 2008 Pearson Education, Inc. 4

Classroom Example 1 Simplifying Higher Roots Find each root. a. = 3, because 33

Classroom Example 1 Simplifying Higher Roots Find each root. a. = 3, because 33 = 27 b. = 6, because 63 = 216 c. = 4, because 44 = 256 Copyright © 2016, 2012, 2008 Pearson Education, Inc. 5

Classroom Example 1 Simplifying Higher Roots (cont. ) Find each root. d. = 3,

Classroom Example 1 Simplifying Higher Roots (cont. ) Find each root. d. = 3, because 35 = 243 e. f. = 0. 4, because 0. 43 = 0. 064 Copyright © 2016, 2012, 2008 Pearson Education, Inc. 6

Objective 2 Find principal roots. Copyright © 2016, 2012, 2008 Pearson Education, Inc. 7

Objective 2 Find principal roots. Copyright © 2016, 2012, 2008 Pearson Education, Inc. 7

Find principal roots. Copyright © 2016, 2012, 2008 Pearson Education, Inc. 8

Find principal roots. Copyright © 2016, 2012, 2008 Pearson Education, Inc. 8

Classroom Example 2 Finding Roots Find each root. =6 a. b. = – 6

Classroom Example 2 Finding Roots Find each root. =6 a. b. = – 6 c. =2 d. = – 2 =3 = – 3 Not a real number Copyright © 2016, 2012, 2008 Pearson Education, Inc. 9

Objective 3 Graph functions defined by radical expressions. Copyright © 2016, 2012, 2008 Pearson

Objective 3 Graph functions defined by radical expressions. Copyright © 2016, 2012, 2008 Pearson Education, Inc. 10

Graph functions defined by radical expressions. A radical expression is an algebraic expression that

Graph functions defined by radical expressions. A radical expression is an algebraic expression that contains radicals. Square Root Function Copyright © 2016, 2012, 2008 Pearson Education, Inc. 11

Graph functions defined by radical expressions. Cube Root Function Copyright © 2016, 2012, 2008

Graph functions defined by radical expressions. Cube Root Function Copyright © 2016, 2012, 2008 Pearson Education, Inc. 12

Graphing Functions Defined with Radicals Classroom Example 3 Graph each function, and give its

Graphing Functions Defined with Radicals Classroom Example 3 Graph each function, and give its domain and range. a. Create a table of values. x y – 2 0 – 1 1 0 1. 41 2 2 Copyright © 2016, 2012, 2008 Pearson Education, Inc. 13

Graphing Functions Defined with Radicals (cont. ) Classroom Example 3 Graph each function, and

Graphing Functions Defined with Radicals (cont. ) Classroom Example 3 Graph each function, and give its domain and range. b. Create a table of values. x y – 3 – 1. 587 0 – 1 1 0 2 1 Copyright © 2016, 2012, 2008 Pearson Education, Inc. 14

Objective 4 Find nth roots of nth powers. Copyright © 2016, 2012, 2008 Pearson

Objective 4 Find nth roots of nth powers. Copyright © 2016, 2012, 2008 Pearson Education, Inc. 15

Find nth roots of nth powers. Copyright © 2016, 2012, 2008 Pearson Education, Inc.

Find nth roots of nth powers. Copyright © 2016, 2012, 2008 Pearson Education, Inc. 16

Classroom Example 4 Simplifying Square Roots Using Absolute Value Find each square root. a.

Classroom Example 4 Simplifying Square Roots Using Absolute Value Find each square root. a. b. c. d. Copyright © 2016, 2012, 2008 Pearson Education, Inc. 17

Find nth roots of nth powers. Copyright © 2016, 2012, 2008 Pearson Education, Inc.

Find nth roots of nth powers. Copyright © 2016, 2012, 2008 Pearson Education, Inc. 18

Simplifying Higher Roots Using Absolute Value Classroom Example 5 Find each root. a. b.

Simplifying Higher Roots Using Absolute Value Classroom Example 5 Find each root. a. b. c. d. Copyright © 2016, 2012, 2008 Pearson Education, Inc. 19

Objective 5 Use a calculator to find roots. Copyright © 2016, 2012, 2008 Pearson

Objective 5 Use a calculator to find roots. Copyright © 2016, 2012, 2008 Pearson Education, Inc. 20

Classroom Example 6 Finding Approximations for Roots Use a calculator to approximate each radical

Classroom Example 6 Finding Approximations for Roots Use a calculator to approximate each radical to three decimal places. a. ≈ 4. 123 b. ≈ – 19. 026 c. ≈ 21. 166 d. ≈ 9. 089 Copyright © 2016, 2012, 2008 Pearson Education, Inc. 21

Classroom Example 7 Using Roots to Calculate Resonant Frequency In electronics, the resonant frequency

Classroom Example 7 Using Roots to Calculate Resonant Frequency In electronics, the resonant frequency f of a circuit may be found using the formula shown below, where f is the cycles per second, L is in henrys, and C is in farads. (Henrys and farads are units of measure in electronics. ) Find the resonant frequency f if L = 6 10– 5 and C = 4 10– 9, to the nearest thousand. Copyright © 2016, 2012, 2008 Pearson Education, Inc. 22

Roots and Radicals Roots and Radicals also calledRoots and Radicals Roots and Radicals also called
Roots and Radicals Roots and Radicals also calledRoots and Radicals Roots and Radicals also called
Roots Fibrous Roots Tap Root Primary Root GrowthRoots Fibrous Roots Tap Root Primary Root Growth
ROOT PAT ROOT TES ROOT WGT ROOT FWTROOT PAT ROOT TES ROOT WGT ROOT FWT
lsmod root test root lsmod root test rootlsmod root test root lsmod root test root
ROOT PAT ROOT TES ROOT WGT ROOT FWTROOT PAT ROOT TES ROOT WGT ROOT FWT
lsmod root test root lsmod root test rootlsmod root test root lsmod root test root
ROOT PAT ROOT TES ROOT WGT ROOT FWTROOT PAT ROOT TES ROOT WGT ROOT FWT
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SIMPLIFYING RADICALS Square Roots and Cube Roots DrSIMPLIFYING RADICALS Square Roots and Cube Roots Dr
SIMPLIFYING SQUARE ROOTS Definition of radicals Square rootsSIMPLIFYING SQUARE ROOTS Definition of radicals Square roots
Chapter 7 Roots Radicals and Complex Numbers CopyrightChapter 7 Roots Radicals and Complex Numbers Copyright
Chapter 7 Roots Radicals and Complex Numbers CopyrightChapter 7 Roots Radicals and Complex Numbers Copyright
Chapter 7 Roots Radicals and Complex Numbers CopyrightChapter 7 Roots Radicals and Complex Numbers Copyright
Chapter 7 Roots Radicals and Complex Numbers CopyrightChapter 7 Roots Radicals and Complex Numbers Copyright
Chapter 7 Roots Radicals and Complex Numbers CopyrightChapter 7 Roots Radicals and Complex Numbers Copyright
Chapter 7 Roots Radicals and Complex Numbers CopyrightChapter 7 Roots Radicals and Complex Numbers Copyright
Chapter 7 Roots Radicals and Complex Numbers CopyrightChapter 7 Roots Radicals and Complex Numbers Copyright