2-8 Square Roots and Real Numbers

Objective: To find square roots, to classify numbers, and to graph solutions on the number line.

Drill #26

Rewrite each fraction in simplest form:

1.

2.

3.

20

3

5

4

3

1

7341

9

2

3

2

Perfect Squares

Perfect Squares:

The perfect squares are numbers that have whole number square roots. The first 7 are represented by the squares above.

14

916

2536

49

Squares Tablex x

1 1 11 121

2 4 12 144

3 9 13 169

4 16 14 196

5 25 15 225

6 36 16 256

7 49 17 289

8 64 18 324

9 81 19 361

10 100 20 400

2x2x

Square Root ** (21.)

Definition: If then x is a square root of y.

NOTE: Once the square root is evaluated, the radical is removed.

Examples:

yx 2

xy

39 525

Classwork

Find the following square roots:

289.8

361.7

256.6

324.5

169.4

Irrational Number

Definition: Numbers that cannot be expressed in the form a/b, where a and b are integers and b = 0.

Irrational numbers are decimals that do not terminate and do not repeat. Square roots of numbers that are not perfect squares are irrational.

Examples:

72

Classwork #26*

Name the set or sets of numbers to which each of the following real numbers belongs:

5

13.12

120.11

16.10

338.0.9

Completeness Property for Points on the Number Line

Definition: Each real number corresponds to exactly one point on the number line. Each point on the number line corresponds to exactly one real number.

Classwork #26*

Graphing Solution Sets

Use the replacement {-2, -1, 0, 1, 2 } to find a solution set for the following

x > 0

What if we didn’t have a replacement? What would the solution set look like?

Graphing InequalitiesExample x > 5When graphing inequalities1. If graphing > or < or = put an open circle on the

number to indicate that the graph does not include this number.

2. If graphing > or < put an closed circle on the number to indicate that the graph does not include this number.

3. If graphing > or > draw a line pointing to the right to include all larger numbers greater in the solution

4. If graphing < or < draw a line pointing to the left to include all smaller numbers in the solution

5. If graphing =

Graphing inequalities

• The line (graph) should be pointing in the same direction as the inequality.

> > graphs point to the right < < graphs point to the left • < and > get open circles

• < and > get closed circles

• = gets open circles and arrows going right and left

Examples

x = -2

x > -2

x < -2

-3 -2 -1 0 1

-3 -2 -1 0 1

-3 -2 -1 0 1