Lesson 1-3 Compare and Order Real Numbers

Area of Quadrilaterals = s x s

Area of Rug 1 = 7 x 7 = 49

1

2

3

Area of Rug 3 = 6 x 8.5 = 51

Area of Circles = 𝜋 x r²

​

Area of Rug 2 = 3.14 x 4² = 50.27

Irrational Number, not a perfect square. We need to rationalize it by making it a decimal

9

16

3

4

√9

√16

3

4

√9

√16

√12

𝜋

STEP 1: THEY MUST ALL BE IN THE SAME NUMBER FORMAT which will be DECIMALS

𝜋

So 3.14 x 3.14 =

9.8596

=9.9

​

𝜋

9.5

No change

9.5

= 9.6

𝜋

√81

√100

9

10

9.8 x 9.8

= 96.04

9.7 x 9.7

= 94.09

𝜋

9.5

9.8

9.6

9.9

9.7

9

10

STEP 1: THEY MUST ALL BE IN THE SAME NUMBER FORMAT which will be DECIMALS

2.25

3.7

-2.5

-4

√11

√9 <

< √16

3

4

3.2 x 3.2

= 10.24

3.3 x 3.3

= 10.89

2.25

3.7

-2.5

-4

3.3

-5

5

0

36 < 39 <49

​

6 < 39 < 7

​

Closest to 36 so whole number = 7

5.7145…… 25 < 29 < 36

​

Rounds to 5.7 5 < 29 < 6

​

Use approximations to get rational number for square root 29...guess…..

5.4 x 5.4 = 29.16 = too high so 5.3

​

Therefore 5.7145… > square root 29

​

16 < 18 < 25

​

4 < 18 < 5

​

Use approximation to get the rational number….so guess….

4.2 x 4.2 = 17.64 just right

4.3 x 4.3 = 18.49 too high

5.2 No change

-5.6 repeating...rounds to -5.7

3 9/10 changes to 3.9

​

Then square root 21 is between 16 and 25. So approximate 4.6 x 4.6 = 21.16 is close

4.5 x 4.5 = 20.25 which is further way. So 4.6 it is

Negative Square Root

-√57 what this really means is -1 x √57

-√49 < -√57 < -√64

7 < √57 < 8 square root 57 is 8 from 49 and 7 from 64 so let’s approximate a decimal that is halfway between 7 and 8 so…

7.5 x 7.5 = 56.26 a little low (0.74 away from 57)

7.6 x 7.6 = 57.76 a little high (0.76 over 57)

Since 7.5² is closer the square root of -√57 is -7.5