10 3 Multiplying Dividing and Simplifying Radicals 1

10. 3 Multiplying, Dividing, and Simplifying Radicals 1. Multiply radical expressions. 2. Divide radical expressions. 3. Use the product rule to simplify radical expressions.

Product Rule for Radicals If both and are real numbers, then The index (root) must be the same!

Multiply:

Quotient Rule for Radicals If both and are real numbers, then The index (root) must be the same!

Divide:

Divide:

Simplify radicals: Look for the largest perfect square that divides into the radicand evenly. 1 4 9 16 25 36 49 64 81 100

Simplify radicals: 1 4 9 16 25 36 49 64 81 100 Create a factor tower.

Divide by prime numbers! 2, 3, 5, 7, 11, …

Simplify radicals: 1 4 9 16 25 36 49 64 81 100

Simplify radicals: 1 4 9 16 25 36 49 64 81 100

Simplify radicals: 1 4 9 16 25 36 49 64 81 100

Simplify radicals: 1 4 9 16 25 36 49 64 81 100

Simplify. a) b) c) d) Copyright © 2011 Pearson Education, Inc. Slide 10 - 16

Simplify. a) b) c) d) Copyright © 2011 Pearson Education, Inc. Slide 10 - 17

Think… de In si si de ut O Simplify radicals:

In si de si ut O Think: de Simplify radicals:

Simplify: 25∙ 3

Simplify: 16∙ 3

Simplify radicals: 1 8 27 64 125 216 343

Simplify radicals: 1 8 27 64 125 216 343

Simplify: 8∙ 3

Simplify: 1 4 9 16 25 36 49 64 81 100 25∙ 6

Simplify: 1 4 9 16 25 36 49 64 81 100 16∙ 3

Simplify. a) b) c) d) Copyright © 2011 Pearson Education, Inc. Slide 10 - 27

Simplify. a) b) c) d) Copyright © 2011 Pearson Education, Inc. Slide 10 - 28