Copyright © 2008 Pearson Education, Inc Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Adding and Subtracting Radicals 8.3 Adding and Subtracting Radicals Add and subtract radicals. Simplify radical sums and differences. Simplify more complicated radical expressions. 1 2 3 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Add and subtract radicals. Objective 1 Add and subtract radicals. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8.3 - 3

Add and subtract radicals. We add or subtract radicals by using the distributive property. For example, Radicands are different Indexes are different Only like radicals—those which are multiples of the same root of the same number—can be combined this way. The preceding example shows like radicals. By contrast, examples of unlike radicals are Note that cannot be simplified. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8.3 - 4

EXAMPLE 1 Add or subtract, as indicated. Solution: Adding and Subtracting Like Radicals Add or subtract, as indicated. Solution: It cannot be added by the distributive property. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8.3 - 5

Simplify radical sums and differences. Objective 2 Simplify radical sums and differences. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8.3 - 6

Simplify radical sums and differences. Sometimes, one or more radical expressions in a sum or difference must be simplified. Then, any like radicals that result can be added or subtracted. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8.3 - 7

EXAMPLE 2 Add or subtract, as indicated. Solution: Adding and Subtracting Radicals That Must Be Simplified Add or subtract, as indicated. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8.3 - 8

Simplify more complicated radical expressions. Objective 3 Simplify more complicated radical expressions. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8.3 - 9

Simplify more complicated radical expressions. When simplifying more complicated radical expressions, recall the rules for order of operations from Section 1.2. A sum or difference of radicals can be simplified only if the radicals are like radicals. Thus, cannot be simplified further. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8.3 - 10

Simplifying Radical Expressions EXAMPLE 3A Simplify each radical expression. Assume that all variables represent nonnegative real numbers. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8.3 - 11

EXAMPLE 3B Simplifying Radical Expressions (cont’d) Simplify each radical expression. Assume that all variables represent nonnegative real numbers. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8.3 - 12