Roots, Radicals, and Root Functions

Slides:

Advertisements

Similar presentations

10.3 Simplifying Radical Expressions

Advertisements

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

Rational Exponents, Radicals, and Complex Numbers

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

Chapter 15 Roots and Radicals.

6.5 Complex Numbers in Polar Form. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 2 Objectives: Plot complex number in the complex plane. Find the.

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

Copyright © 2009 Pearson Education, Inc. CHAPTER 5: Exponential and Logarithmic Functions 5.1 Inverse Functions 5.2 Exponential Functions and Graphs 5.3.

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

Chapter 1 Functions and Graphs Copyright © 2014, 2010, 2007 Pearson Education, Inc Distance and Midpoint Formulas; Circles.

Chapter 8 Section 1 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.

Slide Copyright © 2009 Pearson Education, Inc. 5.4 The Irrational Numbers and the Real Number System.

Roots and Radicals.

Section 3Chapter 8. 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives Simplifying Radical Expressions Use the product rule for.

Section 2Chapter 8. 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives Rational Exponents Use exponential notation for nth roots.

Chapter 1, Section 6. Finding the Coordinates of a Midpoint  Midpoint Formula: M( (x1+x2)/2, (y1+y2)/2 )  Endpoints (-3,-2) and (3,4)

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

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

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

Chapter 8 Roots and Radicals.

Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.5 – Slide 1.

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.

Chapter 2 Functions and Graphs Copyright © 2014, 2010, 2007 Pearson Education, Inc Distance and Midpoint Formulas; Circles.

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

Chapter 8 Section 1. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Evaluating Roots Find square roots. Decide whether a given root.

Section 1 Part 1 Chapter 5. 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives Integer Exponents – Part 1 Use the product rule.

6.3 Simplifying Radical Expressions In this section, we assume that all variables are positive.

Rational Exponents Evaluate rational exponents. 2.Write radicals as expressions raised to rational exponents. 3.Simplify expressions with rational.

Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1 1 Chapter 9 Quadratic Equations and Functions.

Chapter 8 Section 7. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Using Rational Numbers as Exponents Define and use expressions.

10.4 Adding and Subtracting Radical Expressions. Simplify radical expressions involving addition and subtraction. Objective 1 Slide

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

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.

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

Chapter 1 Functions and Graphs Copyright © 2014, 2010, 2007 Pearson Education, Inc Distance and Midpoint Formulas; Circles.

Copyright © 2007 Pearson Education, Inc. Slide R-1.

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

Section 5.5 Solving Exponential and Logarithmic Equations Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.

Altitude-on-hypotenuse. Find the value of x x 4√3 10 x = 4√3 4√3 x + 10 x x = 163 x x – 48 = 0 (x – 4)(x + 12) = 0 x = 4 x = -12.

Copyright © 2008 Pearson Education, Inc

Chapter 8 Section 3.

Roots, Radicals, and Root Functions

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

Section 1-6 Midpoint and Distance in the Coordinate Plane

Adding, Subtracting, and Multiplying Radical Expressions

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

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

Roots, Radicals, and Root Functions

Adding, Subtracting, and Multiplying Radical Expressions

Simplifying Radical Expressions

Lesson 8-2: Special Right Triangles

Quadratic Equations, Inequalities, and Functions

Roots, Radicals, and Root Functions

Adding, Subtracting, and Multiplying Radical Expressions

Inverse, Exponential and Logarithmic Functions

Section 9.4 Area of a Triangle

Precalculus Essentials

Rational Exponents, Radicals, and Complex Numbers

Roots, Radicals, and Root Functions

Inverse, Exponential and Logarithmic Functions

Roots, Radicals, and Root Functions

Chapter 8 Section 4.

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

Roots, Radicals, and Root Functions

Adding, Subtracting, and Multiplying Radical Expressions

Roots, Radicals, and Root Functions

Presentation transcript:

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

Simplifying Radical Expressions 9.3 Simplifying Radical Expressions

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

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

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

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

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

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

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

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

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

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

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

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

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