start bellwork #. chapter 11-1 p.560 square roots and irrational numbers
TRANSCRIPT
Start Bellwork #
Chapter 11-1 p.560
Square Roots and
Irrational Numbers
1 23
21 1 22 4 23 9
The square of an integer is a perfect square.
The opposite of squaring a number is taking the square root.
Example
For example
asks what number multiplied by itself is equal to 81? That number is 9.
Is there another solution to that problem?
81
Example
For example
asks what number multiplied by itself is equal to 81? That number is 9.
Is there another solution to that problem?
Yes, -9 is also a solution.
81
Simplify each square root
100
16
Simplify each square root
100
16
10
Simplify each square root
100
16
10
-4
Squares and roots Here is a list that will be helpful:
2
2
2
2
2
2
2
2
2
2
2
2
1 1
2 4
3 9
4 16
5 25
6 36
7 49
8 64
9 81
10 100
11 121
12 144
1 1
4 2
9 3
16 4
25 5
36 6
49 7
64 8
81 9
100 10
121 11
144 12
Do you see that squares and square roots are inverses (opposites) of each other?
Estimating square roots
Once we have memorized these squares and their roots, we can estimate square roots that are not perfect squares
For example, what about ?8
Estimating square roots
We find the two perfect squares that are before and after the square root of 8. . .
and
Look at them on a number line:
4
9
5
4
96 7 832
2 3
Estimating square roots
We can see that is between 2 and 3 but
is closer to 3. We would say that is approximately 3.
4 5 96 7 832
2 3
8
8
TRY THIS:Estimate to the nearest whole number
27
78
50
TRY THIS:Estimate to the nearest whole number
27
78
50
5
TRY THIS:Estimate to the nearest whole number
27
78
50
5
-9
TRY THIS:Estimate to the nearest whole number
27
78
50
5
-9
7
Rational number- can be written as a fraction
Irrational number- cannot be written as a fraction because:
• it is a non-terminating decimal• it is a decimal that does NOT repeat
* The square roots of ALL perfect squares are rational.
* The square roots of numbers that are NOT perfect squares are irrational.
Try This: Identify each number as rational or irrational
2
81
0.53
0.627
13.875931...
Try This: Identify each number as rational or irrational
2
81
0.53
0.627
13.875931...
Irrational
Try This: Identify each number as rational or irrational
2
81
0.53
0.627
13.875931...
Irrational
Rational
Try This: Identify each number as rational or irrational
2
81
0.53
0.627
13.875931...
Irrational
Rational
Rational
Try This: Identify each number as rational or irrational
2
81
0.53
0.627
13.875931...
Irrational
Rational
Rational
Rational
Try This: Identify each number as rational or irrational
2
81
0.53
0.627
13.875931...
Irrational
Rational
Rational
Rational
Irrational
Agenda
PA#48P.562 #16-35Print out CAT 6 review from my
website or teacherweb.com (P.9-30)