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Warm Up

Preview. Warm Up. California Standards. Lesson Presentation. Warm Up Simplify each expression. 1. 2. 3. 4. California Standards.

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Warm Up

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  1. Preview Warm Up California Standards Lesson Presentation

  2. Warm Up Simplify each expression. 1. 2. 3. 4.

  3. California Standards 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.

  4. You can use the Product and Quotient Properties of square roots you have already learned to multiply and divide expressions containing square roots.

  5. 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.

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

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

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

  9. Check It Out! Example 1b Multiply. Write the product in simplest form. All variables represent nonnegative numbers. Expand the expression. Commutative Property of Multiplication Product Property of Square Roots Simplify the radicand. Simplify the square root. Multiply.

  10. Check It Out! Example 1c Multiply. Write the product in simplest form. All variables represent nonnegative numbers. Factor 14m. Product Property of Square Roots Product Property of Square Roots Simplify.

  11. Distribute Additional Example 2A: Using the Distributive Property Multiply. Write the product in simplest form. All variables represent nonnegative numbers. 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.

  12. Distribute Additional Example 2B: Using the Distributive Property Multiply. Write the product in simplest form. All variables represent nonnegative numbers. Product Property of Square Roots Simplify the radicands. Simplify.

  13. Distribute Check It Out! Example 2a Multiply. Write the product in simplest form. All variables represent nonnegative numbers. 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.

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

  15. 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.

  16. Remember! First terms Outer terms Inner terms Last terms See Lesson 7-8.

  17. = 20 + 3

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

  19. 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.

  20. Check It Out! Example 3a Multiply. Write the product in simplest form. Expand the expression. Use the FOIL method. Simplify by combining like terms.

  21. Check It Out! Example 3b Multiply. Write the product in simplest form. Use the FOIL method. Simplify by combining like terms.

  22. 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.

  23. 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.

  24. Additional Example 4B: 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. Simplify the square root in denominator.

  25. Helpful Hint Use the square root in the denominator to find the appropriate form of 1 for multiplication.

  26. Check It Out! Example 4a Simplify the quotient. Multiply by a form of 1 to get a perfect-square radicand in the denominator. Simplify the square root in denominator.

  27. Check It Out! Example 4b Simplify the quotient. Multiply by a form of 1 to get a perfect-square radicand in the denominator. Simplify the square root in denominator.

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

  29. Lesson Quiz Multiply. Write each product in simplest form. All variables represent nonnegative numbers. 1. 2. 3. 4. 5. 6. 7. Simplify each quotient. All variables represent nonnegative numbers. 8. 9.

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