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Roots Worksheet - PowerPoint

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					  Roots of Real
Numbers and Radical
   Expressions
 Definition of           n th   Root
  For any real numbers a and b
  and any positive integers n,
  if an = b,
  then a is the nth root of b.

** For a square root the value of n is 2.
 Notation
                            radical
index
             4
                  81
                           radicand

Note: An index of 2 is understood but not
      written in a square root sign.
                    4
Simplify                81
To simplify means to find x
      in the equation:
           x 4 = 81

                4
    Solution:       81=   3
       Principal Root
 The nonnegative root of a number

 64         Principal square root
            Opposite of principal
 64        square root
 64        Both square roots
  Summary of Roots
The n th root of b b               n


n b >0 b <0 b =0
       one + root    no real
even   one - root     roots      one real
                                  root, 0
odd    one + root   no + roots
       no - roots   one - root
  Examples
              13 x            
                               2 2
                                      13x   2
1.  169 x   4




2. -   8 x - 3
                   4
                            8 x  3 
                                       2 2




                          8 x  3
                                        2
     Examples
3.   3
         125 x  6       3
                             5 x 
                                 2 3
                                        5x   2




           m n   mn    mn
      3      3       3       3         3
4.
   Taking   nth
              roots of variable
           expressions
    Using absolute value signs

If the index (n) of the radical is
even, the power under the radical
sign is even, and the resulting
power is odd, then we must use an
absolute value sign.
   Examples
Even                            Odd
                     Even


             an   an
                4
        4
   1.
Even
                     Even   Odd


             xy    xy
               2 6          2
   2.   6
Even                           Odd
         2            Even

   3.        x   6
                      x   3
                                       Odd

  Even
                                     Even

                 3  y            3 - y    
                        2 18                  2 3
       4.    6

                               3
                  3 - y    2

				
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