1. Square Roots and Real Numbers
Algebra I ~ Chapter 2-7
Square Roots and Real Numbers

2. SQUARE ROOTS A square root is one of two equal factors of a number.
For example, one square root of 64 is 8 since 8 ∙ 8 (or 82) is 64.
Another square root of 64 is -8 since -8 ∙ -8 or (-8)2 is also 64.
64 is an example of a perfect square.

3. Square Roots
The symbol is called a radical sign and is used to indicate a nonnegative or principal square root of the expression under the radical sign.

4. Perfect Squares up to 15 12 = 1 62 = 36 112 = 121
12 = = = 121
22 = = = 144
32 = = = 169
42 = = = 196
52 = = = 225

5. Find each square root -4 1.)
2.)
3.)
12 (NOTE: When the question asks for just the square root as in #1, this indicates that they are looking for the principal square root, which means the nonnegative square root answer.) -4

6. Find each square root
1.)
2.)
3.) 15
-11

7. Find each square root
1.)
2.)
0.6
-0.08

8. Estimating Square Roots
Example – Estimate
Figure out which “perfect squares”
falls between. In this case, falls between and , thus falling between the whole numbers 4 and 5.
A good estimate would be 4.4 or 4.5 because 20 is almost between 16 and 25.

9. Estimating Square Roots
Example – Estimate
Figure out which “perfect squares”
falls between. In this case, falls between and , thus falling between the whole numbers 9 and 10.
A good estimate would be 9.1 or 9.2 because 83 is closer to 81 than it is to 100.

12. Classifying numbers by sets:
1.)
2.)
3.)
4.)
Irrational
Rational
Integer
Non-real number

13. Graphing Real Numbers
Graph each solution set
1.) y ≥ -3
2.) a < 0

14. Classwork
2.7 Study Guide and Intervention Worksheet