Roots, Radicals, and Root Functions

Slides:

Advertisements

Similar presentations

Roots of Real Numbers and Radical Expressions. Definition of n th Root ** For a square root the value of n is 2. For any real numbers a and b and any.

Advertisements

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

Section 7.1 Basic of Roots (Radicals). Definition of a Square Root if and only if is a square root of.

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

Roots of Real Numbers and Radical Expressions. Definition of n th Root ** For a square root the value of n is 2. For any real numbers a and b and any.

Multiplying, Dividing, and Simplifying Radicals Multiply radical expressions. 2.Divide radical expressions. 3.Use the product rule to simplify radical.

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

Slide Copyright © 2012 Pearson Education, Inc.

11-3 Simplifying Radical Expressions Standard 2.0 One Property.

Section 9.1: Evaluating Radical Expressions and Graphing Square Root and Cube Root Functions.

Checking Factoring  The checking of factoring can be done with the calculator.  Graph the following expressions: 1.x 2 + 5x – 6 2.(x – 3)(x – 2) 3.(x.

Slide 7- 1 Copyright © 2012 Pearson Education, Inc.

Section 1Chapter 8. 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives Radical Expressions and Graphs Find roots of numbers. Find.

Chapter 10 Exponents & Radicals Phong Chau. Section 10.1 Radical Expressions & Functions.

Chapter 8 Section 2 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.

Exponents and Radicals Digital Lesson. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 Repeated multiplication can be written in.

HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Hawkes Learning Systems: Developmental.

Roots of Real Numbers and Radical Expressions. Definition of n th Root ** For a square root the value of n is 2. For any real numbers a and b and any.

You should know or start to recognize these: 2 2 = 43 2 = 94 2 = = = 83 3 = = = = = = = = 323.

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2015, 2011, 2007 Pearson Education, Inc. 1 1 Chapter 8 Rational Exponents, Radicals, and Complex Numbers.

Copyright © 2015, 2011, 2007 Pearson Education, Inc. 1 1 Chapter 8 Rational Exponents, Radicals, and Complex Numbers.

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 15 Roots and Radicals.

HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Hawkes Learning Systems: Developmental.

Radical Basics We will work with square roots, thus, you do not need to write the index. The index for square roots is 2.

1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-1 Basic Concepts Chapter 1.

Chapter P Prerequisites: Fundamental Concepts of Algebra 1 Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1 P.3 Radicals and Rational Exponents.

Intermediate Algebra Chapter 7. Section 7.1 Opposite of squaring a number is taking the square root of a number. A number b is a square root of a number.

5.5 Roots of Real Numbers Squares Roots Nth Roots Principal Roots.

Radical Expressions and Functions Find the n th root of a number. 2.Approximate roots using a calculator. 3.Simplify radical expressions. 4.Evaluate.

Copyright © 2011 Pearson Education, Inc. Rational Exponents and Radicals Section P.3 Prerequisites.

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

7.1 Radicals and Radical Functions. Square Roots Opposite of squaring a number is taking the square root of a number. A number b is a square root of a.

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

1 Chapter 5, Section 5 Roots of Real Numbers. 2 Simplify Radicals Finding the square root of a number and squaring a number are inverse operations. To.

Section 1Chapter 8. 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives Radical Expressions and Graphs Find roots of numbers. Find.

Sections 8.1 and 8.2 Radical Expressions Rational Exponents.

TOPIC 18.1 Radical Expressions

6-1 Radical Functions & Rational Exponents

Simplifying Radical Expressions (10-2)

5.5 Roots of Real Numbers Definitions Simplifying Radicals

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

MTH 100 Radical Expressions.

Roots, Radicals, and Root Functions

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Roots of Real Numbers and Radical Expressions

Roots, Radicals, and Complex Numbers

Chapter 8 – Roots, Radicals and Rational Functions

Section 2.5 Graphing Techniques; Transformations

7. Roots and Radical Expressions

Section 1.2 Exponents & Radicals

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Objectives Rewrite radical expressions by using rational exponents.

Roots of Real Numbers and Radical Expressions

Copyright © 2013 Pearson Education, Inc. All rights reserved

Section 2.5 Graphing Techniques; Transformations

Radicals and Radical Functions

Introduction to Radicals Radical Expressions Finding a root of a number is the inverse operation of raising a number to a power. This symbol is the radical.

Roots, Radicals, and Root Functions

Roots, Radicals, and Root Functions

Roots & Radical Expressions

Roots and Radical Expressions

Radicals and Radical Functions

Roots, Radicals, and Complex Numbers

Roots, Radicals, and Root Functions

Piecewise-defined Functions

Roots, Radicals, and Root Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Rational Exponents and Radicals

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.