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Multiplying, Dividing, and Simplifying Radicals 10.3 1.Multiply radical expressions. 2.Divide radical expressions. 3.Use the product rule to simplify radical expressions.

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

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Multiply:

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Quotient Rule for Radicals If both and are real numbers, then

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Divide:

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Divide:

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

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

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

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

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

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

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

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

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

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Simplify radicals: Outside Inside Outside Inside Think…

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Simplify radicals: Outside Inside Think:

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Simplify: 25∙3

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Simplify: 16∙3

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1 8 27 64 125 216 343 Simplify radicals:

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1 8 27 64 125 216 343 Simplify radicals:

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Simplify: 8∙3

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

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

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

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

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