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```									Roots and Irrational Number

expressions, the student will be able to
determine rationality and approximate
value with 80% accuracy.
Check For Understanding

1. 25               4
4.
25
2. 196
40
5.
3. 169             10
Where does the   1 1        2 4
Term “Perfect      1          2
Square”
Come from?       5 25       8 64
5          8

Conclusion?      A “Perfect Square”
refers to the area of a
square with a given side
length…
Where does the   1 1        2 4
Term “Square       1          2
Root” come from?
5 25        8 64
5           8

Conclusion?      A “Square Root” refers
to length of the side of a
square with a given
area…
12 22 32 42 52 62 72
What are the        1 4 9 16 25 36 49
“Perfect Squares”
for 1 through 20?   82 92 102 112 122 132
64 81 100 121 144 169
And 25 squared?
142 152 162 172 182
196 225 256 289 324

192 202 … 252
361 400 … 625
Taking the
“Square Root”

64          64 (= 8 • 8) = 8
16          16 (= 4 • 4 ) = 4
121         121 (= 11 • 11) = 11
9            9=3
1           1 (= 1 • 1) = 1
Taking the
“Square Root”
Of a number
That is not a
Perfect square:

67              67  8.185352772…

10              10  3.16227766…
150             150  12.24744871…
Conclusion:       These roots are “irrational”
What is the
A non-repeating AND
definition of an
non-terminating decimal…
irrational
number?

What rule have     Taking the square root of
we discovered      A perfect square will always
About square       Give an integer…but taking
Roots?             The square toot of any other
Number will always give an
Irrational number…
What is a square
root spiral?
Check For Understanding

1. 25             4         4
4.    
25         25
2. 196
40
5.
3. 169             10
Check For Understanding

1.  5           4. 
2
5
2.  14
5.  2
3.  13

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