Estimating Square Roots

1
Estimating Square Roots

• Unit One
• (sec 1.4)
• Lesson 03
• Koomens Klass

2
The square root of a number is just a number
which when multiplied by itself gives you back
your original number.
So 2 is the square root of 4 because 2 x 2 4.
BUT . . . some numbers do not have a perfect
square root ?
How can we determine the square root of a number
that is NOT square?
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How???
Start with the number you want to find the
square root of. Let's use 12.
There are four steps
1. guess
2. divide
3. average
4. check
. . . do it once, then just keep repeating
steps 2 thru 4 until you are happy ?
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Step 1 Guess
Since 32 9 and 42 16 . . .you know the
answer is somewhere between these two values
might as well try the exact middle . . .
3.5
5
Step 2 Divide

3.42857
12
3.5
without a calculator, you must use long
division . . . YIKES!
6
.
3.5
1 2 . 0 0 0 0
.
0
0
3
4
2
so . . .
35.
1 2 0 . 0 0 0
-1 0 5
Dont forget!
1 5
0
-1 4 0
1 0
0
-7 0
etc . . .
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Step 3 Average
work out the average of 3.5 and 3.42857
3.5
.
7
5
8
6
9
2
2


3.42857
3.464285
.
7
5
8
6
9
2
of course . . .
without a calculator, you must use long division
. . . Ha! Ha! Ha!
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Step 4 Check
3.464285
3.464285
x
12.00127
Yay!!! That looks pretty good to me!
so . . . the square root of 12 is
approximately 3.46
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PRACTICE. . .
Read text pages 22 thru 24.
Work carefully through the examples.
Answer all questions on p. 26 27

• Show your work
• Check your answers