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11-4 Multiplying and Dividing Radical Expressions Warm Up Warm Up Lesson Presentation Lesson Presentation California Standards California StandardsPreview

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11-4 Multiplying and Dividing Radical Expressions Warm Up Simplify each expression. 1. 2. 3. 4.

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11-4 Multiplying and Dividing Radical Expressions Extension of 2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents. California Standards

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11-4 Multiplying and Dividing Radical Expressions You can use the Product and Quotient Properties of square roots you have already learned to multiply and divide expressions containing square roots.

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11-4 Multiplying and Dividing Radical Expressions Additional Example 1A: Multiplying Square Roots Multiply. Write the product in simplest form. All variables represent nonnegative numbers. Product Property of Square Roots Multiply the factors in the radicand. Factor 16 using a perfect-square factor. Product Property of Square Roots Simplify.

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11-4 Multiplying and Dividing Radical Expressions Additional Example 1B: Multiplying Square Roots Expand the expression. Commutative Property of Multiplication Product Property of Square Roots. Simplify the radicand. Simplify the square root. Multiply. Multiply. Write the product in simplest form. All variables represent nonnegative numbers.

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11-4 Multiplying and Dividing Radical Expressions Additional Example 1C: Multiplying Square Roots Simplify the radicand. Factor 12 using a perfect-square factor. Product Property of Square Roots Simplify. Multiply. Write the product in simplest form. All variables represent nonnegative numbers.

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11-4 Multiplying and Dividing Radical Expressions Check It Out! Example 1a Product Property of Square Roots Multiply the factors in the radicand. Factor 50 using a perfect-square factor. Product Property of Square Roots Multiply. Write the product in simplest form. All variables represent nonnegative numbers.

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11-4 Multiplying and Dividing Radical Expressions Check It Out! Example 1b Expand the expression. Commutative Property of Multiplication Product Property of Square Roots Simplify the radicand. Simplify the square root. Multiply. Multiply. Write the product in simplest form. All variables represent nonnegative numbers.

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11-4 Multiplying and Dividing Radical Expressions Check It Out! Example 1c Product Property of Square Roots Factor 14m. Product Property of Square Roots Simplify. Multiply. Write the product in simplest form. All variables represent nonnegative numbers.

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11-4 Multiplying and Dividing Radical Expressions Additional Example 2A: Using the Distributive Property Product Property of Square Roots. Multiply the factors in the second radicand. Factor 24 using a perfect-square factor. Product Property of Square Roots Simplify. Distribute Multiply. Write the product in simplest form. All variables represent nonnegative numbers.

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11-4 Multiplying and Dividing Radical Expressions Additional Example 2B: Using the Distributive Property Product Property of Square Roots Distribute Simplify the radicands. Simplify. Multiply. Write the product in simplest form. All variables represent nonnegative numbers.

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11-4 Multiplying and Dividing Radical Expressions Check It Out! Example 2a Product Property of Square Roots Multiply the factors in the first radicand. Factor 48 using a perfect-square factor. Product Property of Square Roots Simplify. Distribute Multiply. Write the product in simplest form. All variables represent nonnegative numbers.

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11-4 Multiplying and Dividing Radical Expressions Check It Out! Example 2b Product Property of Square Roots Factor 50 using a perfect-square factor. Simplify. Distribute Multiply. Write the product in simplest form. All variables represent nonnegative numbers.

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11-4 Multiplying and Dividing Radical Expressions In Chapter 7, you multiplied binomials by using the FOIL method. The same method can be used to multiply square-root expressions that contain two terms.

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11-4 Multiplying and Dividing Radical Expressions First terms Outer terms Inner terms Last terms See Lesson 7-8. Remember!

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11-4 Multiplying and Dividing Radical Expressions = 20+ 3

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11-4 Multiplying and Dividing Radical Expressions Additional Example 3A: Multiplying Sums and Differences of Radicals Multiply. Write the product in simplest form. Use the FOIL method. Simplify the radicand. Simplify by combining like terms. Simplify.

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11-4 Multiplying and Dividing Radical Expressions Additional Example 3B: Multiplying Sums and Differences of Radicals Multiply. Write the product in simplest form. Expand the expression. Use the FOIL method. Simplify by combining like terms.

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11-4 Multiplying and Dividing Radical Expressions Check It Out! Example 3a Multiply. Write the product in simplest form. Expand the expression. Use the FOIL method. Simplify by combining like terms.

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11-4 Multiplying and Dividing Radical Expressions Check It Out! Example 3b Multiply. Write the product in simplest form. Use the FOIL method. Simplify by combining like terms.

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11-4 Multiplying and Dividing Radical Expressions A quotient with a square root in the denominator is not simplified. To simplify these expressions, multiply by a form of 1 to get a perfect-square radicand in the denominator. This is called rationalizing the denominator.

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11-4 Multiplying and Dividing Radical Expressions Additional Example 4A: Rationalizing the Denominator Simplify the quotient. All variables represent nonnegative numbers. Multiply by a form of 1 to get a perfect- square radicand in the denominator. Product Property of Square Roots Simplify the denominator.

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11-4 Multiplying and Dividing Radical Expressions Additional Example 4B: Rationalizing the Denominator Simplify the square root in denominator. Multiply by a form of 1 to get a perfect- square radicand in the denominator. Simplify the quotient. All variables represent nonnegative numbers.

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11-4 Multiplying and Dividing Radical Expressions Use the square root in the denominator to find the appropriate form of 1 for multiplication. Helpful Hint

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11-4 Multiplying and Dividing Radical Expressions Check It Out! Example 4a Simplify the quotient. Simplify the square root in denominator. Multiply by a form of 1 to get a perfect- square radicand in the denominator.

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11-4 Multiplying and Dividing Radical Expressions Check It Out! Example 4b Simplify the quotient. Simplify the square root in denominator. Multiply by a form of 1 to get a perfect- square radicand in the denominator.

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11-4 Multiplying and Dividing Radical Expressions Check It Out! Example 4c Simplify the quotient. Simplify the square root in denominator. Multiply by a form of 1 to get a perfect- square radicand in the denominator. Factor and simplify the square root in the numerator.

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11-4 Multiplying and Dividing Radical Expressions Lesson Quiz 1. 3. 5. 2. 4. 6. 7. Multiply. Write each product in simplest form. All variables represent nonnegative numbers. 8.9. Simplify each quotient. All variables represent nonnegative numbers.

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