Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 9.5 - 1.

Slides:

Advertisements

Similar presentations

Warm Up Simplify each expression

Advertisements

Simplifying Radical Expressions Product Property of Radicals For any numbers a and b where and,

Multiplying and Dividing Radial Expressions 11-8

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

10.5 Multiplying and Dividing Radical Expressions

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

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

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

Objectives Multiply and divide radical expressions.

Multiplying and Dividing Radial Expressions 11-8

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

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

Identify the perfect square in each set , 81, 27, , 99, 8, , 84, 12, , 216, 196, 72 Find the Prime Factorization of.

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

WARM UP POWER OF A PRODUCT Simplify the expression. 1.(3x) 4 2.(-5x) 3 3.(xy) 6 4.(8xy) 2 4.

R Review of Basic Concepts © 2008 Pearson Addison-Wesley. All rights reserved Sections R.5–R.7.

Notes Over 9.4 Simplifying a Rational Expression Simplify the expression if possible. Rational Expression A fraction whose numerator and denominator are.

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

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 © 2010 Pearson Education, Inc. All rights reserved Sec

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

11-4 Multiplying and Dividing Radical Expressions Warm Up Warm Up Lesson Presentation Lesson Presentation California Standards California StandardsPreview.

Including Rationalizing The Denominators. Warm Up Simplify each expression

Copyright © 2010 Pearson Education, Inc. All rights reserved Sec Rational Expressions and Functions Chapter 8.

Copyright © Cengage Learning. All rights reserved. Roots, Radical Expressions, and Radical Equations 8.

Copyright 2013, 2009, 2005, 2001, Pearson, Education, Inc.

SIMPLIFYING RADICAL EXPRESSIONS

Chapter 8 Section 5 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.

Chapter 9 Section 4 Dividing Square Roots. Learning Objective 1.Understand what it means for a square root to be simplified 2.Use the Quotient Rule to.

Conjugate of Denominator

To divide radicals: divide the coefficients divide the radicands if possible rationalize the denominator so that no radical remains in the denominator.

Conjugate: Value or that is multiplied to a radical expression That clears the radical. Rationalizing: Removing a radical expression from the denominator.

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.

Chapter 11 Sec 1 Simplifying Radical Expressions.

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

Advanced Algebra Notes Section 4.5: Simplifying Radicals (A) A number r is a _____________ of a number x if. The number r is a factor that is used twice.

Rationalizing Numerators and Denominators of Radical Expressions Rationalize denominators. 2.Rationalize denominators that have a sum or difference.

7.5 Operations with Radical Expressions. Review of Properties of Radicals Product Property If all parts of the radicand are positive- separate each part.

Copyright © 2012, 2008, 2004 Pearson Education, Inc. 1 Objectives Multiplying and Dividing Radical Expressions Multiply radical expressions. Rationalize.

3.9 Mult/Divide Rational Expressions Example 1 Multiply rational expressions involving polynomials Find the product. Multiply numerators and denominators.

Homework Multiply. Write each product in simplest form. All variables represent nonnegative numbers Simplify each quotient.

Chapter 6 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 6-1 Rational Expressions and Equations.

Warm Up Simplify each expression

Multiplying and Dividing Radial Expressions 11-8

Roots, Radicals, and Root Functions

Multiplying and Dividing Radial Expressions 11-8

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

Multiplying and Dividing Radical Expressions

11.4 Multiply & Divide Radical Expressions

Simplifying Radical Expressions

Multiplying and Dividing Radial Expressions 11-8

Copyright © 2008 Pearson Education, Inc

Rational Expressions and Functions

Rational Expressions and Functions

Mult/Divide Rational Expressions

Simplifying Radical Expressions

Chapter 8 Section 5.

Warm Up Simplify each expression

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

Complex Rational Expressions

1.2 Multiply and Divide Radicals

Simplifying Radical Expressions

10-1 Simplifying Radicals

Chapter 8 Section 4.

Dividing Radical Expressions

Simplifying Radical Expressions

Roots, Radicals, and Root Functions

Chapter 8 Section 5.

Presentation transcript:

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

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

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

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Multiplying and Dividing Radical Expressions Objectives 1.Multiply radical expressions. 2.Rationalize denominators with one radical term. 3.Rationalize denominators with binomials involving radicals. 4.Write radical quotients in lowest terms.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Multiplying and Dividing Radical Expressions Multiply Radical Expressions Multiplication of expressions that contain radicals is very similar to multiplication of polynomials.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Multiplying and Dividing Radical Expressions Multiply Radical Expressions Multiplication of expressions that contain radicals is very similar to multiplication of polynomials.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Multiplying and Dividing Radical Expressions Multiply Radical Expressions Multiplication of expressions that contain radicals is very similar to multiplication of polynomials. FOIL Method

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Multiplying and Dividing Radical Expressions Rationalize Denominators with One Radical Term A simplified radical expression has no radical in the denominator. The process of removing a radical from the denominator of a fractional expression is called rationalizing the denominator.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Multiplying and Dividing Radical Expressions Rationalize Denominators with Square Roots Rationalize the following:

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Multiplying and Dividing Radical Expressions Rationalize Denominators with Cube Roots To rationalize a denominator with a cube root, we must multiply the numerator and denominator by a number that will result in a perfect cube.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Multiplying and Dividing Radical Expressions Rationalize Denominators with Binomials Involving Radicals

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Multiplying and Dividing Radical Expressions Rationalize Denominators with Binomials Involving Radicals

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Multiplying and Dividing Radical Expressions Rationalize Denominators with Binomials Involving Radicals

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Multiplying and Dividing Radical Expressions Writing Radical Quotients in Lowest Terms CAUTION Be careful to factor before writing a quotient in lowest terms.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Multiplying and Dividing Radical Expressions Writing Radical Quotients in Lowest Terms CAUTION Be careful to factor before writing a quotient in lowest terms.