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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Description: Roots Worksheet document sample