A.9 nth Roots and Solving with Radicals
The secret impresses no one. The trick you use it for is everything.
-Alfred Borden
nth Roots
The principal nth root of a number a, is defined as follows:
n



a b
means
ab
n
 If n  2 is even, a  0 and b  0
 If n  3 is odd, a and b are any real numbers


Evaluating nth Roots
1)
5
32
2)
3
64
3)
4
1
16
4)
2
(4) 4
Properties of Radicals
(1)
n
(2)
(3)
ab  n a n b
n
n
Ex: 32
a na
 n 
b
b
Ex:
3
 
Ex:
3
a 
m
n
m
a

5
8
8
5

Simplifying Radicals
1)
3
16x 4 y10
2)

72x 5 y 8
Simplifying Radicals
3)
3
36x 4 y  3 60x 3 y 2
Multiplying and Combining Radicals


1) 2 6 5 30

2)

 5  3 5  2
Rationalizing Denominators
When quotients have radicals, it is customary to rewrite the
quotient so that the denominator contains no roots.
Here are some examples of how to get rid of the roots!
1)
3
2)
52
3)
2 1
4)
3
4
Rationalizing Denominators
1)
2)
2
2
7


7
7
7
14

49
14

7

3 1
2 33
Solving Equations with Roots
Solve the following equation.
3

1 3t  2  0
A.9 nth Roots and Rational Exponents
Homework#11 : p.1038
#35-49 odd
The secret impresses no one. The trick you use it for is everything.
-Alfred Borden