Radical Expressions by yurtgc548

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									Roots and Irrational Number

    OBJECTIVE: Given 5 radical
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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