Section 13 2 Adding Subtracting and Multiplying Radical

Section 13. 2 Adding, Subtracting, and Multiplying Radical Expressions Copyright © 2011 Pearson Education, Inc.

Radical Expressions Combining Like Radicals Example Combine like radicals Solution Copyright © 2011 Pearson Education, Inc. Section 13. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 2

Radical Expressions Combining Like Radicals Solution Example Continued 3. Since the radicals have different indexes, we cannot use the distributive law • It’s already simplified 4. Since the radicals have different radicands, we cannot use the distributive law • It’s already simplified Example Perform the indicated operations. Copyright © 2011 Pearson Education, Inc. Section 13. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 3

Radical Expressions Combining Like Radicals Solution Copyright © 2011 Pearson Education, Inc. Section 13. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 4

Radical Expressions Combining Like Radicals Solution Continued Copyright © 2011 Pearson Education, Inc. Section 13. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 5

Radical Expressions Adding or Subtracting Radical Expressions Example Perform the indicated operation. Solution Copyright © 2011 Pearson Education, Inc. Section 13. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 6

Radical Expressions Adding or Subtracting Radical Expressions Solution Example Continued Perform the indicated operation. Copyright © 2011 Pearson Education, Inc. Section 13. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 7

Multiplying Radical Expressions Finding Products of Radical Expressions Example Find the product. Solution Copyright © 2011 Pearson Education, Inc. Section 13. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 8

Multiplying Radical Expressions Finding Products of Radical Expressions Solution Example Continued Copyright © 2011 Pearson Education, Inc. Section 13. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 9

Multiplying Radical Expressions Finding Products of Radical Expressions Solution Example Continued If is defined, then In words: The nth power of the nth root of a number is the number. Example Simplify. Copyright © 2011 Pearson Education, Inc. Section 13. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 10

Multiplying Radical Expressions Simplifying Radical Expressions Solution 1. Multiply each term of the first factor by each term of the second factor, and combine like radicals: Copyright © 2011 Pearson Education, Inc. Section 13. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 11

Multiplying Radical Expressions Simplifying Radical Expressions Solution Continued Example Simplify . Copyright © 2011 Pearson Education, Inc. Section 13. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 12

Multiplying Radical Expressions Simplifying the Square of a Radical Expression with Two Terms Solution Another way: Copyright © 2011 Pearson Education, Inc. Section 13. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 13

Multiplying Radical Expressions Simplifying the Square of a Radical Expression with Two Terms Warning Example Simplify Solution Copyright © 2011 Pearson Education, Inc. Section 13. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 14

Multiplying Radical Expressions Example Find the product. Solution Copyright © 2011 Pearson Education, Inc. Section 13. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 15

Multiplying Radical Expressions Solution Example Continued Find the product. Copyright © 2011 Pearson Education, Inc. Section 13. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 16

Multiplying Radical Expressions Multiplying Two Radicals with Different Indexes but the Same Radicand Process To multiply two radicals that have the different index, we use the product property: Copyright © 2011 Pearson Education, Inc. Section 13. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 17

Multiplying Radical Expressions Multiplying Two Radicals with Different Indexes but the Same Radicand Process To multiply two radicals with different indexes but the same radicand, 1. Write the radicals in exponential form. 2. Use exponential properties to simplify the expression involving exponents. 3. Write the simplified expression in radical form. Copyright © 2011 Pearson Education, Inc. Section 13. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 18

Multiplying Radical Expressions Simplify Radical Expressions Example Perform the indicated operations. Assume that x ≥ 0. Solution Copyright © 2011 Pearson Education, Inc. Section 13. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 19

Multiplying Radical Expressions Simplify Radical Expressions Solution Example Continued Perform the indicated operations. Assume that x ≥ 0. Copyright © 2011 Pearson Education, Inc. Section 13. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 20

Multiplying Radical Expressions Simplify Radical Expressions Process To simplify a radical expression, 1. Perform any indicated multiplications. 2. Combine like radicals. 3. For any radical with index n, write the radicand as a product of one or more perfect nth powers and another expression that has no factors that are perfect nth powers. Then apply the product property for radicals. 4. Write any radicals with as small an index as possible. Copyright © 2011 Pearson Education, Inc. Section 13. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 21