algebra i ~ chapter 2-7 square roots and real numbers
TRANSCRIPT
Algebra I ~ Algebra I ~ Chapter 2-7Chapter 2-7
Square Roots and Real Square Roots and Real NumbersNumbers
SQUARE ROOTSSQUARE 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.
Square RootsSquare Roots The symbol is called a The symbol is called a
radical sign and is used to radical sign and is used to indicate a nonnegative or indicate a nonnegative or principal square rootprincipal square root of the of the expression under the radical expression under the radical sign. sign.
Perfect Squares up to Perfect Squares up to 151512 = 1 62 = 36 112 = 121
22 = 4 72 = 49 122 = 144
32 = 9 82 = 64 132 = 169
42 = 16 92 = 81142 = 196
52 = 25 102 = 100152 = 225
Find each square rootFind each square root
16
25
9
1441.)
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.)
5
3
25
9
-4
Find each square rootFind each square root
121
100
144
2251.)
2.)
3.)
15
10
12
100
144
-11
5
6
Find each square rootFind each square root
0064.0
36.01.)
2.)
0.6
-0.08
Estimating Square RootsEstimating Square Roots
20
20
16
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.
2025
Estimating Square RootsEstimating Square Roots
83
83
81
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.
83100
Classifying numbers by Classifying numbers by sets:sets:
9
1
169
171.)
2.)
3.)
4.)
Irrational
Rational
324
Integer
Non-real number
Graphing Real Graphing Real NumbersNumbers
Graph each solution set
1.) y ≥ -3
2.) a < 0
ClassworkClasswork
2.7 Study Guide and Intervention 2.7 Study Guide and Intervention WorksheetWorksheet