Transcript perfect squares

Welcome to Homeroom
• Read quietly starting @ 9 o’clock.
Math Support
• Opening
– Continue to work on Estimating and Graphing
Non-perfect Squares
Evaluating Squares and Square
Roots
Example 1:
y2=25
x2=64
Evaluating Squares and Square
Roots
Example 2:
Homework Check
• Have TOC #2 out on your desk
Perfect Squares
1)
25 5
2)
4)
144 12
4
2
5)
169 13
49 7
8)
225
7)
10) 100 10
13) 4900 70
16) 121 11
19) 81 9
15
11) 36 6
14) 9 3
17) 1600 40
20) 14400 120
3) 1 1
6) 900 30
9) 16  4
12) 196 14
15) 64 8
18) 400 20
21) 10000 100
Non-Perfect Squares
Here is the list of perfect squares from 1 to 256.
1 1
25  5
81  9
169  13
4 2
36  6
100  10
196  14
9 3
49  7
121  11
225  15
16  4
64  8
144  12
256  16
Not every number is a perfect square. If they
aren’t, we call them non-perfect squares. To
find the square root of a number that is not a
perfect square, we use estimation with perfect
squares.
Non-Perfect Squares
Yesterday, we tried to make a perfect square out
of 10 squares and couldn’t do it.
But there is an answer to the square root of 10.
We just have to use what we know about the
perfect squares to find it.
25  5
16  4
4 2
9 3
1 1
Using the above information (which we should
have memorized), what two numbers would
the answer to 10 be between?
Since 10 is between 9 and 16, the answer to 10 is
between the answer to 9 and the answer to 16 .
Non-Perfect Squares
Since 10 is between 9 and 16, and the answers for
those square roots are 3 and 4, the square root of
10 would be between 3 and 4… probably closer
to 3 because 10 is closer to 9 than 16. It would be
plotted on a number line as below.
9 3
9
3
10
10
3.5
3.162277…
16  4
16
4
While the calculator answer is there, the point should be
able to be placed without the calculator… not exactly,
but on the left side of the halfway point.
To find the square root of a number with a TI
calculator:
1) Press the “2nd” button
2) Press the “x2” button
3) Type the number you wish to find the square root
of.
4) Press “Enter” or “=”
Is the calculator correct when it gives you an
answer? Click HERE for the answer on the next
slide.
To find the square root of a number with a TI
calculator:
1) Press the “2nd” button
2) Press the “x2” button
3) Type the number you wish to find the square root
of.
4) Press “Enter” or “=”
Is the calculator correct when it gives you an
answer?
If you tried to find the answer to the square root of a
non-perfect square number, the calculator is only
correct until its last digit. The real answer to the
square root of a non-perfect square number is a
decimal that goes on forever (non-terminating)
without repeating (non-repeating). So the last digit
that the calculator shows is rounded… close, but not
perfect or exact.
Graphing and Estimating
Practice
Closing
• Summarize how to estimate and graph
square roots. Provide an example.
1. TOC
2. 9-18-12 Perfect Squares Worksheet
• Copy in agenda
#2 Perfect Squares Worksheet
You need graph paper and colored pencils.
OPENING: Solve for x, show your work.
2x  5  6x 19
(on graph paper)
Square Roots
radicand
radical
Practice!
I Have Who Has?
Perfect Squares
Lengths Perfect
Squares
1x1
1
2x2
4
3x3
9
4x4
16
15
225
Square Root
What is the area?
• A square with side lengths 8 units
• Side lengths 6 units
• Side lengths 0.05 units
What is the side length?
• A square with an area of 144 units2
• An area of 49 units2
• An area of 6400 units2
More Examples*
(5)
2
 6
2
( y)
2
 m
2
Homework!!!
Closing
• http://www.brainpop.com/math/numbersan
doperations/squareroots/