1. SQUARE ROOTS

2. This isn’t exactly true, but for the next 3 weeks: “Radical” means the same thing as “square root” *Side Note:

3. What is a square root?

4. A square root is a way of asking: “What number, times itself gives this value?”

5. What is a square root? A square root is a way of asking: “What number, times itself gives this value?” “What number times itself is 25?”

6. What is a square root? A square root is a way of asking: “What number, times itself gives this value?” “What number times itself is 25?” “5 times 5 is 25.”

7. “What number times itself is 25?” “5 times 5 is 25.” * This is called “taking the square root.” * Notice, after we have taken the square root, the symbol is gone.

8. These are the numbers that have a “nice” answer when we take a square root:

9. What number times itself is 1? These are the numbers that have a “nice” answer when we take a square root:

10. What number times itself is 4? These are the numbers that have a “nice” answer when we take a square root:

11. What number times itself is 9? These are the numbers that have a “nice” answer when we take a square root:

12. What number times itself is 16? These are the numbers that have a “nice” answer when we take a square root:

13. What number times itself is 25? These are the numbers that have a “nice” answer when we take a square root:

14. What number times itself is 36? These are the numbers that have a “nice” answer when we take a square root:

16. Since these numbers give nice answers, we call them perfect squares. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144

17. Since these numbers give nice answers, we call them perfect squares. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144

18. Since these numbers give nice answers, we call them perfect squares. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 You will have to know these numbers.

19. Since these numbers give nice answers, we call them perfect squares. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 You will have to know these numbers. Do I have to memorize them?

20. Since these numbers give nice answers, we call them perfect squares. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 You will have to know these numbers. Do I have to memorize them? You can, but… It is probably easier to just remember how we get them: You can, but… It is probably easier to just remember how we get them:

21. Since these numbers give nice answers, we call them perfect squares. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 You will have to know these numbers. Do I have to memorize them? You can, but… It is probably easier to just remember how we get them: You can, but… It is probably easier to just remember how we get them: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 Just square the numbers 1-12.

22. So, if you have a problem that looks like this:

23. Just write the number that answers the question:

24. So, if you have a problem that looks like this: Just write the number that answers the question: “What number times itself is 16?”

25. So, if you have a problem that looks like this: Just write the number that answers the question: “What number times itself is 16?” 4

26. The hard part is when the answer is not obvious:

27. No nice number times itself is 20.

28. The hard part is when the answer is not obvious: No nice number times itself is 20. There are two options for how to find the square root of 20.

29. The hard part is when the answer is not obvious: No nice number times itself is 20. Option 1Get an approximate answer (decimal) You just type it in the calculator. (easy) There are two options for how to find the square root of 20.

30. The hard part is when the answer is not obvious: No nice number times itself is 20. Option 1Get an approximate answer (decimal) You just type it in the calculator. (easy) Option 2 The exact answer. This is like reducing a fraction (hard) There are two options for how to find the square root of 20.

31. The hard part is when the answer is not obvious: No nice number times itself is 20. Option 1Get an approximate answer (decimal) You just type it in the calculator. (easy) Option 2 The exact answer. This is like reducing a fraction (hard) There are two options for how to find the square root of 20. You will have to be able to do BOTH.

32. Option 1Get an approximate answer (decimal) You just type it in the calculator. (easy)

33. Use the square root button here to just type it in the calculator.

34. Option 1Get an approximate answer (decimal) You just type it in the calculator. (easy) Use the square root button here to just type it in the calculator. Did you get 400? Make sure to hit the “ctrl” key first!

35. Option 1Get an approximate answer (decimal) You just type it in the calculator. (easy) Use the square root button here to just type it in the calculator. Did you get 400? Make sure to hit the “ctrl” key first!

36. Option 1Get an approximate answer (decimal) You just type it in the calculator. (easy) This isn’t the best answer, because the calculator had to round the answer.

37. Option 1Get an approximate answer (decimal) You just type it in the calculator. (easy) This isn’t the best answer, because the calculator had to round the answer. That’s why we call it “approximate” That’s why we call it “approximate”

38. Option 2Get an EXACT answer A square root is a lot like a fraction. There are many different ways to write the same number.

39. Option 2Get an EXACT answer A square root is a lot like a fraction. There are many different ways to write the same number. For example:

40. Option 2Get an EXACT answer A square root is a lot like a fraction. There are many different ways to write the same number. For example:

41. Option 2Get an EXACT answer For example:

42. Option 2Get an EXACT answer For example: Just like with fractions, all these are the same thing. But they are not reduced.

43. Option 2Get an EXACT answer For example: Like fractions, there is a BEST ANSWER We call it a reduced radical

44. Option 2Get an EXACT answer

45. You learned how to reduce the radical in algebra 1

46. Option 2Get an EXACT answer You learned how to reduce the radical in algebra 1 There are two good ways:

47. Option 2Get an EXACT answer You learned how to reduce the radical in algebra 1 There are two good ways: Method 1 the factor tree (this is easy, but takes a long time) https://www.youtube.com/watch?v=jC5-2FOCXGg Method 2 using perfect squares. (Faster, but not as easy to remember) https://www.youtube.com/watch?v=sOmnOQn5HsU

48. Option 2Get an EXACT answer You learned how to reduce the radical in algebra 1 There are two good ways: Method 1 the factor tree (this is easy, but takes a long time) https://www.youtube.com/watch?v=jC5-2FOCXGg Method 2 using perfect squares. (Faster, but not as easy to remember) https://www.youtube.com/watch?v=sOmnOQn5HsU Watch one or both of the videos

49. Option 2Get an EXACT answer You learned how to reduce the radical in algebra 1 There are two good ways: Method 1 the factor tree (this is easy, but takes a long time) https://www.youtube.com/watch?v=jC5-2FOCXGg Method 2 using perfect squares. (Faster, but not as easy to remember) https://www.youtube.com/watch?v=sOmnOQn5HsU I don’t get it! And I hate that guy in the video. What do I do? I don’t get it! And I hate that guy in the video. What do I do?

50. Option 2Get an EXACT answer You learned how to reduce the radical in algebra 1 There are two good ways: Method 1 the factor tree (this is easy, but takes a long time) https://www.youtube.com/watch?v=jC5-2FOCXGg Method 2 using perfect squares. (Faster, but not as easy to remember) https://www.youtube.com/watch?v=sOmnOQn5HsU I don’t get it! And I hate that guy in the video. What do I do? I don’t get it! And I hate that guy in the video. What do I do? A)Ask Mr. B for help. B) Type “simplify square roots” into youtube. 15,000 hits! A)Ask Mr. B for help. B) Type “simplify square roots” into youtube. 15,000 hits!

51. #1 on your worksheet Here is how to do it

52. #1 on your worksheet Here is how to do it

53. #1 on your worksheet Here is how to do it

54. #1 on your worksheet Here is how to do it

55. #1 on your worksheet Here is how to do it

56. #1 on your worksheet Here is how to do it

57. #1 on your worksheet Here is how to do it

58. Or do it this way:

59. #1 on your worksheet

60. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 Perfect squares:

61. #1 on your worksheet 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 Perfect squares: Find the biggest perfect square you can divide 20 by and NOT get a decimal

62. #1 on your worksheet 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 Perfect squares: Find the biggest perfect square you can divide 20 by and NOT get a decimal It’s 4

63. #1 on your worksheet 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 Perfect squares: Find the biggest perfect square you can divide 20 by and NOT get a decimal It’s 4 Rewrite the square root using the perfect square times a number

64. #1 on your worksheet 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 Perfect squares: Find the biggest perfect square you can divide 20 by and NOT get a decimal It’s 4 Rewrite the square root using the perfect square times a number

65. #1 on your worksheet 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 Perfect squares: Find the biggest perfect square you can divide 20 by and NOT get a decimal It’s 4 Rewrite the square root using the perfect square times a number Take the square root of the perfect square.

66. #1 on your worksheet 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 Perfect squares: Find the biggest perfect square you can divide 20 by and NOT get a decimal It’s 4 Rewrite the square root using the perfect square times a number Take the square root of the perfect square.

67. #1 on your worksheet DONE

68. You should now be able to do problems 1-12 Use either method

69. Other side of your paper (multiplying square roots)

71. Part 2 Multiplying square roots

72. When we multiply two square roots

73. Part 2 Multiplying square roots When we multiply two square roots Multiply the numbers in the square root

74. Part 2 Multiplying square roots When we multiply two square roots Multiply the numbers in the square root

75. Part 2 Multiplying square roots

76. Then, we have to see if this square root can be reduced

77. Part 2 Multiplying square roots (this is just like #1)

78. Part 2 Multiplying square roots (this is just like #1)

79. Now, do problems 13-15

80. For this type of problem, we have regular numbers AND square roots being multiplied

81. Multiply the regular numbers first

82. For this type of problem, we have regular numbers AND square roots being multiplied Multiply the regular numbers first

83. For this type of problem, we have regular numbers AND square roots being multiplied Multiply the regular numbers first

84. For this type of problem, we have regular numbers AND square roots being multiplied Multiply the regular numbers first Next, multiply the square roots

85. For this type of problem, we have regular numbers AND square roots being multiplied Multiply the regular numbers first Next, multiply the square roots

86. For this type of problem, we have regular numbers AND square roots being multiplied Multiply the regular numbers first Next, multiply the square roots

87. For this type of problem, we have regular numbers AND square roots being multiplied Multiply the regular numbers first Next, multiply the square roots Then, simplify the square root.

88. For this type of problem, we have regular numbers AND square roots being multiplied Multiply the regular numbers first Next, multiply the square roots Then, simplify the square root.

89. For this type of problem, we have regular numbers AND square roots being multiplied Multiply the regular numbers first Next, multiply the square roots Then, simplify the square root.

90. For this type of problem, we have regular numbers AND square roots being multiplied Multiply the regular numbers first Next, multiply the square roots Then, simplify the square root. Bring back the regular number

91. For this type of problem, we have regular numbers AND square roots being multiplied Multiply the regular numbers first Next, multiply the square roots Then, simplify the square root. Bring back the regular number

92. For this type of problem, we have regular numbers AND square roots being multiplied Multiply the regular numbers first Next, multiply the square roots Then, simplify the square root. Bring back the regular number Finally, re-multiply the regular numbers

93. For this type of problem, we have regular numbers AND square roots being multiplied Multiply the regular numbers first Next, multiply the square roots Then, simplify the square root. Bring back the regular number Finally, re-multiply the regular numbers

94. Now, do problems 16-18

96. This is an easy one.

97. “squared” means multiply be itself.

98. This is an easy one. “squared” means multiply be itself.

99. This is an easy one. “squared” means multiply be itself.

100. This is an easy one. “squared” means multiply be itself. What number times itself is 64?

101. This is an easy one. “squared” means multiply be itself. What number times itself is 64?

102. This is an easy one. “squared” means multiply be itself. What number times itself is 64? There is a very simple pattern to these problems

103. Do problems 19-21 (Yes, they are very easy)

104. This is just like the last one, but there is a regular number too!

105. Write it out

106. This is just like the last one, but there is a regular number too! Write it out

107. This is just like the last one, but there is a regular number too! Write it out Multiply the regular numbers

108. This is just like the last one, but there is a regular number too! Write it out Multiply the regular numbers

109. This is just like the last one, but there is a regular number too! Write it out Multiply the regular numbers Multiply the square roots

110. This is just like the last one, but there is a regular number too! Write it out Multiply the regular numbers Multiply the square roots

111. This is just like the last one, but there is a regular number too! Write it out Multiply the regular numbers Multiply the square roots

112. Do problems 22-24 (there is an easy pattern here, too.)

114. Rationalizing the denominator This is BAD. We are not allowed to have a square root in the denominator (bottom of a fraction) We will have problems that end like this, and we have to know how to fix ‘em

115. How to get rid of a square root on the bottom of a fraction You can’t leave “root 2” in the bottom of the fraction What is “root 2” times “root 2”? This is how you have to leave your answers

116. 1. 2. 3. 4. 5.

118. To get rid of the square root on the bottom of a fraction…

119. …Multiply the top and bottom of the fraction by the square root you are trying to get rid of.

120. To get rid of the square root on the bottom of a fraction… …Multiply the top and bottom of the fraction by the square root you are trying to get rid of.

121. To get rid of the square root on the bottom of a fraction… …Multiply the top and bottom of the fraction by the square root you are trying to get rid of.

122. To get rid of the square root on the bottom of a fraction… …Multiply the top and bottom of the fraction by the square root you are trying to get rid of. Then reduce the regular numbers

123. To get rid of the square root on the bottom of a fraction… …Multiply the top and bottom of the fraction by the square root you are trying to get rid of. Then reduce the regular numbers

124. To get rid of the square root on the bottom of a fraction… …Multiply the top and bottom of the fraction by the square root you are trying to get rid of. Then reduce the regular numbers

125. Do problems 25-28