Section 3.3

The Real Number System

By definition 25 is the number you would multiply times itself to get 25 for an answer.

Because we are familiar with multiplication, we know that 25 = 5

Numbers like 25, which have whole numbers for their square roots, are called perfect squares

Perfect square

Square root

1 1 = 1

4 4 = 2

9 9 = 3

16 16 = 4

25 25 = 5

36 36 = 6

49 49 = 7

64 64 = 8

81 81 = 9

100 100 = 10

121 121 = 11

144 144 = 12

169 169 = 13

196 196 = 14

225 225 = 15

Perfect square

Square root

Every whole number has a square root

Most numbers are not perfect squares, and so their square roots are not whole numbers.

Most numbers that are not perfect squares have square roots that are irrational numbers

Irrational numbers can be represented by decimals that do not terminate and do not repeat

Rational + Irrational = REAL Numbers

Obj: To find the square root of a number

• Find the square roots of the given numbers

• If the number is not a perfect square, use a calculator to find the answer correct to the nearest thousandth.

81

37

158

81 = 9

37 6.083

158 12.570

Obj: To find the square root of a number

• Find two consecutive whole numbers that the given square root is between

• Try to do this without using the table

18

115

18 is between 4 and 5

115 is between 10 and 11

16 = 4 and 25 = 5 so

100 = 10 and 121 = 11 so

Obj: To find the square root of a number

• Find two consecutive whole numbers that the given square root is between

• Try to do this without using the table

29

73

29 is between 5 and 6

73 is between 8 and 9

25 = 5 and 36 = 6 so

64 = 8 and 81 = 9 so

Obj: To find the square root of a number

• Find two consecutive whole numbers that the given square root is between

• Try to do this without using the table

150

55

150 is between 12 and 13

55 is between 7 and 8

144 = 12 and 169 = 13 so

49 = 7 and 64 = 8 so

Graphing real numbers

The graph of a number is a dot placed where the number would be on the number line

0 5 10-5-10

Graph the number: 3 5 -- 12

0 5 10-5-10

Graph the number: -8.5

Classwork / Homework

Page 128 # 32 – 48 Even

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