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Splash Screen. Five-Minute Check (over Lesson 6–4) CCSS Then/Now New Vocabulary Key Concept: Product Property of Radicals Example 1: Simplify Expressions with the Product Property Key Concept: Quotient Property of Radicals Example 2: Simplify Expressions with the Quotient Property

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 6–4) CCSS Then/Now New Vocabulary Key Concept: Product Property of Radicals Example 1: Simplify Expressions with the Product Property Key Concept: Quotient Property of Radicals Example 2: Simplify Expressions with the Quotient Property Concept Summary: Simplifying Radical Expressions Example 3: Multiply Radicals Example 4: Add and Subtract Radicals Example 5: Multiply Radicals Example 6: Real-World Example: Use a Conjugate to Rationalize a Denominator Lesson Menu

  3. A. 11h B. 11h2 C. 13h2 D. –11h 5-Minute Check 1

  4. A. B.–4ay3 C. D.8ay3 5-Minute Check 2

  5. A. B. C. D. 5-Minute Check 3

  6. A. |m – 4| B.m – 4 C. |m – 2| D.m – 2 5-Minute Check 4

  7. A. about 1.43 m B. about 2.52 m C. about 3.11 m D. about 5.48 m 5-Minute Check 5

  8. Between which two whole numbers is ? A. 10 and 11 B. 11 and 12 C. 12 and 13 D. 13 and 14 5-Minute Check 6

  9. Content Standards A.SSE.2 Use the structure of an expression to identify ways to rewrite it. Mathematical Practices 1 Make sense of problems and persevere in solving them. CCSS

  10. You simplified expressions with nth roots. • Simplify radical expressions. • Add, subtract, multiply, and divide radical expressions. Then/Now

  11. rationalizing the denominator • like radical expressions • conjugate Vocabulary

  12. Concept

  13. Simplify. Answer: Simplify Expressions with the Product Property Factor into squares where possible. Product Property of Radicals Example 1

  14. Answer: Simplify Expressions with the Product Property Factor into cubes. Product Property of Radicals Simplify. Example 1

  15. A. Simplify . A. B. C. D. Example 1

  16. A. B. C. D. Example 1

  17. Concept

  18. A. Simplify Expressions with the Quotient Property Quotient Property Factor into squares. Product Property Example 2

  19. Rationalize the denominator. Simplify Expressions with the Quotient Property Answer: Example 2

  20. Rationalize the denominator. Simplify Expressions with the Quotient Property Quotient Property Product Property Example 2

  21. Simplify Expressions with the Quotient Property Multiply. Answer: Example 2

  22. A. Simplify . A. B. C. D. Example 2

  23. B. Simplify A. B. C. D. Example 2

  24. Concept

  25. Multiply Radicals Product Property of Radicals Factor into cubes where possible. Product Property of Radicals = 5 ● 10 ● a or 50a Multiply. Answer: 5 ● 10 ● a or 50a Example 3

  26. A. 12a B. 24a C. 4a D. 6a Example 3

  27. Answer: Add and Subtract Radicals Factor using squares. Product Property Multiply. Combine like radicals. Example 4

  28. A. B. C. D. Example 4

  29. Simplify . F O I L Product Property Answer: Multiply Radicals Example 5

  30. Simplify . A. B. C. D. Example 5

  31. GEOMETRY In a square with side a, the ratio of a side to the difference between the diagonal and a side is . Use a conjugate to rationalize the denominator and simplify . Use a Conjugate to Rationalize a Denominator Example 6

  32. Use a Conjugate to Rationalize a Denominator Multiply. Simplify. Factor out the GCF. Example 6

  33. Use a Conjugate to Rationalize a Denominator Simplify. Example 6

  34. GEOMETRY In the triangle shown with height x, the ratio of the height to the base is . Use a conjugate to rationalize the denominator and simplify . A. B. C.D. Example 6

  35. End of the Lesson

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