Transcript non-perfect squares

Learning Goal:
Identify the two consecutive whole numbers
between which the square root
of a non-perfect square whole number
less than 225 lies
(with and without the use of a number line)
Perfect Squares (a review)
1)
25
2)
169
4)
144
4
5)
49
3) 1
6) 900
8)
225
9) 16 
7)
10) 100
13) 4900
16) 121
19) 81
11) 36
14) 9
17) 1600
20) 14400
12) 196
15) 64
18) 400
21) 10000
Perfect Squares (a review)
1)
25 5
4)
144 12
4
2
7)
10) 100 10
13) 4900 70
16) 121 11
19) 81 9
Answers
2) 169 13
5)
49
7
3) 1 1
6) 900 30
8)
225
15
9) 16  4
11) 36 6
14) 9 3
17) 1600 40
20) 14400 120
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
Using dot paper try to make a perfect square out of
10 squares. Can you do it?
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 right 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.
Working with
“Uncomfortable” Numbers
 Approximation

A value close to the
true value but rounded
to a whole number or
decimal that is more
reasonable to work
with.
Ex) 3.1415926…
becomes
3.14
 Estimate

The result of a
calculation using
approximated values.
The answer will be
reasonably close to the
true value.
Ex)
5.378 x 6.581
becomes 5 x 7 = 35
Assignment
How to obtain the square root
of an imperfect square?
Shortcut:
Let’s say we need to calculate the square root of
95.
Let’s understand the steps:
Step 1 : By looking at the number itself,
we can guess, the square root of 95 lies
between 9 and 10.
So, √95=9.__
Step 2 : 95 is 14 more than 92.
Add 14 divided by twice the integer part
of the square root
i.e., 9×2 = 18.
So, the approximate square root of 95 is 9.77
which is very close to 9.747
which is the actual square-root of 95.
Consider another example, Let’s say we
need to calculate the square root of 150.
Step 1 : The square root of 150 lies
between 12 and 13.
So, √150=12.__
Step 2 : 150 is 6 more than 122.
Add 6 divided by twice the
integer part of the square root
i.e., 12×2 = 24.
So, the approximate square root of 150 is 12.25
which is very close to 12.247
which is the actual square-root of 150.
Using the same shortcut, can you obtain the
square roots of
a) 300
b) 250
c) 600
d) 242