1. Unit 2. Day 11.

2. Please get out paper for today’s lesson
Name
Date
Period
Topic: Irrational numbers
8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2)

3. Today’s Lesson Perfect Squares and Cube Roots
2) Approximating Non-Perfect Square Roots
[Irrational Numbers]
3) Simplifying Square Roots
4) Comparisons involving irrational numbers

4. Square Roots = 1 1
1 2 =1
Because = 4 2
2 2 =4
Because = 9 3
3 2 =9
Because = 16 4
4 2 =16
Because = 64 8
8 2 =64
Because =
144 12
12 2 =144
Because

5. = = = −1 ? −4 ? −9 ? 2 =−1 ? 2 =−4 ? 2 =−9 ? Square Roots Because

6. Square Roots 9 16 25 ? 1 4 ? ?

7. Cube Roots =
3 1 1
1 3 =1
Because =
3 8 2
2 3 =8
Because =
3 27 3
3 3 =27
Because =
3 64 4
4 3 =64
Because =
3 125 5
5 3 =125
Because =
3 216 6
6 3 =216
Because

8. Cube Roots =
3 −1 −1
−1 3 =−1
Because =
3 −8 −2
−2 3 =−8
Because =
3 −27 −3
−3 3 =−27
Because =
3 −64 −4
−4 3 =−64
Because =
3 −125 −5
−5 3 =−125
Because =
3 −216 −6
−6 3 =−216
Because

9. Cube Roots
3 0
3 −8
3 −27
3 64
3 343
3 −1
3 1
3 8
3 27

11. Today’s Lesson Perfect Squares and Cube Roots
2) Approximating Non-Perfect Square Roots
[Irrational Numbers]
3) Simplifying Square Roots
4) Comparisons involving irrational numbers

12. Place the numbers 2 and 3 on the number line.
Place the numbers 5 , 6 , 7 , & 8 on the number line.
Place the numbers , , 12 , , , & on the number line. 2 3 5 6 7 8 10 12 14 11 13 15 1 4 9 16

13. 49 =7 Example A: Determine 49 . 7 × 7 4 9
[If the number is not a perfect square, determine which whole number the square root would be closest to, and then use guess and check to give an approximate answer to one or two decimal places]
49 =7 7 × 7
4 9

14. Could we get more accurate?
Example B: Determine
[If the number is not a perfect square, determine which whole number the square root would be closest to, and then use guess and check to give an approximate answer to one or two decimal places] 62 9 7
7.5
7.8 8 81 49 64
Could we get more accurate? 5 6 6 8
62 ≈7.9
7.8
7.9 ×
7.8 ×
7.9 6 2 4 7 1 1 1 1 + 5 4 6 ∎ + 5 5 3 ∎ . . 6 8 4 6 2 4 1

15. 62 ≈7.87 . . Example B: Determine 62 . 7.9 7.7 7.8 7.8 7 7.8 8 × 7.8 7
[If the number is not a perfect square, determine which whole number the square root would be closest to, and then use guess and check to give an approximate answer to one or two decimal places] 62
7.9
7.7
7.8
7.85
60.84
62.41 6 6 6 5 4 4 6 7 7 6 6 5
7.8 7
7.8 8
62 ≈7.87 ×
7.8 7 ×
7.8 8 2 5 5 9 6 3 4 1 6 2 9 6 ∎ 6 3 4 ∎ 1 1 5 + 5 9 ∎ ∎ 5 5 + 1 6 ∎ ∎ . . 6 1 9 3 6 9 6 2 9 4 4

16. 78 121 38 Example C: Example D: Example E: Determine the square root.
[If the number is not a perfect square, determine which whole number the square root would be closest to, and then use guess and check to give an approximate answer to one or two decimal places] 78
Example C:
121
Example D: 38
Example E:

17. 78 ≈8.8 . . . Example C: Determine 78 . 8.5 9 7 8 8.7 8.8 8.9 × 8.7 ×
[If the number is not a perfect square, determine which whole number the square root would be closest to, and then use guess and check to give an approximate answer to one or two decimal places] 78
8.5 9 7 8 81 49 64
78 ≈8.8 5 6 7 4 6 8
8.7
8.8
8.9 ×
8.7 ×
8.8 ×
8.9 6 9 7 4 8 1 1 + 6 9 6 ∎ + 7 4 ∎ + 7 1 2 ∎ . . . 7 5 6 9 7 7 4 4 7 9 2 1

18. 121 =11 Example D: Determine 121 . 11 × 11 121
[If the number is not a perfect square, determine which whole number the square root would be closest to, and then use guess and check to give an approximate answer to one or two decimal places]
121 =11 11 × 11
121

19. Could we get more accurate?
Example E: Determine
[If the number is not a perfect square, determine which whole number the square root would be closest to, and then use guess and check to give an approximate answer to one or two decimal places] 38 8 6
6.5 7 64 36 49
Could we get more accurate? 1
62 ≈6.2
6.2
6.1 ×
6.2 ×
6.1 1 2 4 6 1 1 + 3 7 2 ∎ + 3 6 6 ∎ . . 3 8 4 4 3 7 2 1

20. Example E: Determine
[If the number is not a perfect square, determine which whole number the square root would be closest to, and then use guess and check to give an approximate answer to one or two decimal places] 38
6.2
6.0
6.1
6.15
38 ≈6.16
60.84
62.41 1 1 4 4 3 3 2 3
6.1 7
6.1 6
6.1 5 ×
6.1 7 ×
6.1 6 ×
6.1 5 4 1 3 1 9 3 1 6 9 6 3 1 7 5 6 1 7 ∎ 6 1 6 ∎ 6 1 5 ∎ 1 1 1 3 + 7 2 ∎ ∎ 3 + 6 9 6 ∎ ∎ 3 6 + 9 ∎ ∎ . . . 3 8 6 8 9 3 7 9 4 5 6 3 7 8 2 2 5

22. Today’s Lesson Perfect Squares and Cube Roots
2) Approximating Non-Perfect Square Roots
[Irrational Numbers]
3) Simplifying Square Roots
4) Comparisons involving irrational numbers

23. Simplifying Square Roots81 81 = 9
9 ∙9 = 9 3 ∙ 9 = 3 = 9 16 16 = 4 =
4 ∙4 = 4 2 ∙ 4 2 = 4 64 64 = 8 =
4∙4∙4 = 4 2 ∙ 4 2 ∙ 4 2 = 8 24 24
2∙12 = 2 ∙ 12 = = ? = ?
4∙6 = 4 2 ∙ 6 = =
2 6 =
3∙8 = 3 ∙ 8 = ?

24. Example F: Simplifying Square Roots24 = 2 ∙ 2 ∙ 2 ∙ 3 6
2 6

25. Example G: Simplifying Square Roots75 = 3 ∙ 5 ∙ 5 3
5 3

26. Example H: Simplifying Square Roots48 = 2 ∙ 2 ∙ 2 ∙ 2 ∙ 3 3
4 3

28. Today’s Lesson Perfect Squares and Cube Roots
2) Approximating Non-Perfect Square Roots
[Irrational Numbers]
3) Simplifying Square Roots
4) Comparisons involving irrational numbers

29. Decide which is greater (<,>,=):
𝜋 2 9 𝜋
> 3
Example I:

30. Decide which is greater (<,>,=):50 51
Example J:

31. Decide which is greater (<,>,=):50 8
Example K:

32. < −2𝜋 −6 𝜋 > 3 2𝜋 > 6 −6 −2𝜋 >
Decide which is greater (<,>,=):
<
−2𝜋 −6 𝜋
> 3 2𝜋
> 6 −6
−2𝜋
>
Example L:

33. Example M: Rodney thinks that 3 64 is greater than 17 4
Example M: Rodney thinks that is greater than Sam thinks that is greater. Who is right and why?
17 4
3 64
<
4 1 4 4
<

34. Example N: Which number is smaller, 121 or 3 125 ?
>
3 125 11
> 5

35. No Homework. Study Guide Day Tomorrow.