This preview shows pages 1–5. Sign up to view the full content.
31
L4
nth
Roots; Rational Exponents
nth
Roots
A number
b
is an
nth root
of a number
a
if
n
ba
=
.
The
principal nth root of a real number
a
is
denoted
n
a
(2
)
n
≥
and defined as follows:
If
n
is an even number
and
0
a
≥
, then
n
a
is the nonnegative
n
th root;
0
a
<
, then
n
a
is undefined (not a real number)
If
n
is an odd number
, then
n
a
is the only real
n
th
root of a number
a
and it has the same sign as
a
.
Note
:
Since
n
a
is an
n
th root, then
( )
n
n
aa
=
.
Example
: Evaluate the radical expressions.
3
27
5
32
−
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document 32
4
81
16
−
Cancellation Rule for Exponents and Radicals
:
n
n
aa
=
if
2
n
≥
and
n
is
even
n
n
=
if
3
n
≥
and
n
is
odd
Note
:
2
x
x
=
, not
x
±
.
Example
: Simplify the expressions.
()
4
4
3
−
4
4
3
−
6
6
2
5
5
4
−
33
Rules for Radicals
: (we assume that all radicals are
defined)
()
m
n
m
n
aa
=
nn
n
ab
a
b
=
⋅
n
n
n
b
b
=
m
nm
n
=
kn
n
km
m
=
Example
: Simplify each expression.
3
2
27
10
40
⋅
2
3
64
3
4
12
9
16
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document 34
Simplifying Radicals:
1.
Use the cancellation rule for radicals and exponents
to remove all
possible factors out of the radical.
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 11/07/2011 for the course MAC 1147 taught by Professor German during the Summer '08 term at University of Florida.
 Summer '08
 GERMAN
 Calculus, Exponents

Click to edit the document details