2-8 Square Roots and Real Numbers

1
2-8 Square Roots and Real Numbers

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

2
Drill 26

• Rewrite each fraction in simplest form

3
Perfect Squares

• Perfect Squares
• The perfect squares are numbers that have whole
  number square roots. They are represented by the
  squares above.

1
4
9
16
25
36
49
4
Squares Table
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
5
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

6
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

7
Completeness Property for Real Numbers
8
Graphing Inequalities