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Chapter 9 Section 2 Simplifying Square Roots

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Learning Objective 1.Use the product rule to simplify square roots containing constants 2.Use the product rule to simplify square roots containing variables

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Key Vocabulary product rule for square roots perfect square perfect square factor

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Product Rule to Simplify Square Roots Containing Constants Rule # 1 - Product Rule for Square Roots Example: All are factors of

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Simplify Square Roots Containing Constants 1.Write the constant as a product of the largest perfect square and another factor 2.Use the Product Rule to write the expression as a product of square roots, with each square roots containing one of the factors 3.Find the square root of the perfect square factor

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Product Rule to Simplify Square Roots Containing Constants Examples:

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Product Rule to Simplify Square Roots Containing Constants Examples:

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Product Rule to Simplify Square Roots Containing Constants Examples:

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Product Rule to Simplify Square Roots Containing Constants When working with large radicand may have to continue to simplify Examples:

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Square Roots of a Perfect Square Perfect squares can also be variables when raised to an even exponent Examples: Rule #2: Square Root of a Perfect Square The square root of a variable raised to an even power equals the variable raised to ½ that power.

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Square Roots of Even Power Examples:

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Square Roots of Odd Power To simplify the Square Root of a Radicand Containing a Variable Raised to an Odd Power 1.Express the variable as the product of two factors, one being to the first power this makes the other a perfect square 2.Use the product rule to simplify

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Square Roots of Odd Power Exp.

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Square Roots of Odd Power Exp:

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Square Roots of Odd Power Exp.

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Remember Rule # 1 - Product Rule Even Powers - The square root of a variable raised to an even power equals the variable raised to ½ that power. Odd Powers - Express the variable as the product of two factors, one being to the first power this makes the other a perfect square then use the product rule to simplify.

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Remember Even though we are assuming all variables represent nonnegative real numbers, remember that When simplifying radicals, we sometimes forget to pull numbers outside the radical symbol.

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HOMEWORK 9.2 Page 545 - 546: #15, 25, 27, 31, 33, 35, 39, 47, 55, 57, 65

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