Unit 2. Day 11.

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)

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

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

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

Square Roots 9 16 25 ? 1 4 ? ?

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

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

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

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

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

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

Could we get more accurate? Example B: Determine 62 . [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

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

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:

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

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

Could we get more accurate? Example E: Determine 38 . [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

Example E: Determine 38 . [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

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

Simplifying Square Roots 81 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 = ?

Example F: Simplifying Square Roots 24 = 2 ∙ 2 ∙ 2 ∙ 3 6 2 6

Example G: Simplifying Square Roots 75 = 3 ∙ 5 ∙ 5 3 5 3

Example H: Simplifying Square Roots 48 = 2 ∙ 2 ∙ 2 ∙ 2 ∙ 3 3 4 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

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

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

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

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

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

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

No Homework. Study Guide Day Tomorrow.