1. Simplify: BELLWORK

2. CHECK HOMEWORK

3. RADICALS AND RATIONAL EXPONENTS Evaluate square roots Use the product rule to simplify square roots Use the quotient rule to simplify square roots Add and subtract square roots Rationalize denominators Evaluate and perform operations with higher roots Understand and use rational expressions

4. MIND MAP Radicals/Square Roots

5. SQUARE ROOTS Radical sign Radicand

6. EVALUATE THE SQUARE ROOTS

7. MORE INFORMATION ABOUT SQUARE ROOTS

9. a) Find b) Find c) Based on your answers to parts (a) and (b), what can you conclude? TRY THIS:

10. If a and b represent nonnegative real numbers, then THE PRODUCT RULE FOR SQUARE ROOTS The square root of a product is the product of the square roots The product of two square roots is the square roots of the product of the radicands

11. a) Use a calculator to approximate to two decimal places b) Use a calculator to approximate to two decimal places c) Based on your answers to parts (a) and (b), what can you conclude? TRY THIS:

12. A SIMPLIFIED SQUARE ROOT

13. I DO:

14. WE DO:

15. BELLWORK

16. HOMEWORK:

17. a) Find b) Find c) Based on your answers to parts (a) and (b), what can you conclude? TRY THIS:

18. THE QUOTIENT RULE FOR SQUARE ROOTS The square root of a quotient is the quotient of the square roots The quotient of two square roots is the square root of the quotient of the radicands

19. I DO

20. WE DO

21. YOU DO

22. ADDING AND SUBTRACTING RADICALS To be able to add or subtract radicals, they must have the same radicand and the same index.

23. COMBINING SQUARE ROOTS

24. I DO

25. WE DO

26. YOU DO

27. Sometimes we have to simplify radicals before we can add or subtract them. At first the terms might not look like they can be combined, so we have to simplify first. COMBINING RADICALS THAT REQUIRE SIMPLIFICATION FIRST

28. I DO

29. WE DO

30. YOU DO

31. Add or subtract whenever possible EXIT TICKET

32. TB pg. 46 (#23-43 odd) HOMEWORK:

33. Multiply: (F.O.I.L.) BELLWORK:

34. When we say that we are going to rationalize the denominator, we are rewriting the rational expression so that we no longer have a radical in the denominator. Multiply the numerator and denominator by the smallest number that produces the square root of a perfect square in the denominator. RATIONALIZING THE DENOMINATOR Multiplication by 1 does not change the value of the rational expression. But what does it mean to multiply by 1, and how can this help us rationalize a denominator?

35. I DO

36. WE DO

37. YOU DO

38. CONJUGATES

40. I DO

41. WE DO

42. YOU DO

43. TB pg. 46 (#45-53 odd) CLASS WORK:

44. Finish Class Work: If necessary Quiz next Friday on sections P-2 & P-3 Simplifying exponential and radical expressions HOMEWORK

45. BELLWORK

46. CLASSWORK ANSWERS

47. OTHER ROOTS Radical sign Radicand Index

48. ROOTS OF REAL NUMBERS

49. If n is odd, If n is even, NTH ROOTS OF PERFECT NTH POWERS

50. Evaluate CUBE ROOTS

51. Evaluate 4 TH ROOTS

52. 5 TH ROOTS

53. Evaluate: I DO

54. Evaluate WE DO:

55. Evaluate YOU DO:

56. PRODUCT AND QUOTIENT RULES FOR OTHER ROOTS and

57. I DO

58. Simplify BELLWORK

59. HOMEWORK ANSWERS

60. Adding and subtracting nth roots is very similar to adding and subtracting square roots. Sometimes we will need to simplify first. Remember: They must have the same index and radicand!!!! COMBINING NTH ROOTS

61. Add or subtract whenever possible I DO

62. Add or subtract whenever possible WE DO

63. Add or subtract whenever possible YOU DO

64. GROUP ACTIVITY

65. What rules did your group come up with? How did you get to this rule, what thinking led you there? Do you think this rule will work for every radical? REFLECTION

66. Evaluate without using a calculator BELLWORK

67. HOMEWORK ANSWERS

68. DEFINITIONS

69. Now that we know how to write a radical as a rational exponent, what properties do you think apply?

70. Simplify using properties of exponents I DO:

71. Simplify using properties of exponents WE DO:

72. Simplify using properties of exponents YOU DO:

73. Simplify by reducing the index of the radical. Sometimes, problems are easier to simplify if we can reduce the index first SIMPLIFYING

74. For exponents(p-2): Product Rule Quotient Rule Zero Exponent Rule Negative Exponent Rule Power Rule Power of a product rule Power of a quotient rule Simplifying exponential expressions For Radicals (P-3): Evaluating square and higher roots Product rule for square and higher roots Quotient rule for square and higher roots Adding and subtracting square roots Rationalizing denominators Rational Exponents YOU NEED TO KNOW:

75. TB pg. 86-87 (#24-31) (#41-71) These are just practice problems, they are to help guide you to what you need to study most. I would recommend doing a few from each section to gauge your understanding QUIZ REVIEW

76. TB pg. 46-47 (#83-107 odd) Study for tomorrow’s quiz HOMEWORK: