Download 7.1 Roots and Radical Expressions

7.1 Roots and Radical Expressions
Review: Properties of Exponents
1
n
0
a  n
a  1, a  0
a
a m  a n  a m n
m
a
m n
a
n
a
a 
ab  a b
n
m n
n n
n
a  a
 
n
b b
n
a
mn
Review: Examples
  
1. 3a 2 4a 6


2.  4 x 2  2 x 2


5 4 3
3. 2 x y
8a 5
4.
2a 2

Review: Examples
6 x7 y5
5.
3 x 1
 3x 2 

6. 

2



2r
7.
2

-1 2 0  2
s t
2rs
Roots
For any real numbers a and b, and any positive integer n,
if a n  b, then a is an n th root of b.
Example : Since 5  125, 5 is a cube root of 125.
3
radical sign
index
n
a
radicand
Possible Real Roots n
#
EXAMPLES:
A NUMBER IS POSITIVE
If n is even, there are
If n is odd, there is
16
4 16
16
5
real roots.
3
real root.
16
A NUMBER IS 0
If n is even, there is
real root.
If n is odd, there is
real root.
3
A NUMBER IS NEGATIVE
If n is even, there are
real roots.
If n is odd, there is
real root.
3
0
4
0
0
5
0
 27
4
 27
 27
5
 27
calc
Roots
When a number has two real roots, the positive root
is called the principle root.
Ex: Find the principle fourth root of 16.
Roots
Find each REAL number root (vs. find ALL real number roots).
1)
49
2) 3
8
3)
4
81
4) 3
 27
5)
 100
Simplifying
n
a  a when n is even
n
Simplify each radical expression.
4x
2
7)
4x
6
8) 3
a 3b 6
6)
9)
4
4 8
x y
Simplifying
Simplify each radical expression.
4x2 y 4
10)
11)
3
 27c 6
12) 4
x8 y12
7.1 Roots and Radical Expressions
HW 7.1: 1-49 odd, Challenge: 51, 53