Math 1513 Sec R.7
1
Section
R.7
Radical Notation and Rational Exponents
If
2
x
a
then
x
a
or
x
a
.
If
n
x
a
then
x
is said to be an nth root of
a
(
n
x
a
).
Symbols like
3
6
,
,
are called radicals.
Properties of Radicals
1.
If
n
is even,
 
n
n
a
a
.
2.
If
n
is odd,
n
n
a
a
.
3.
n
n
n
a
b
ab
.
4.
(
0)
n
n
n
b
a
b
a
b
.
5.
(
)
m
n
n
m
a
a
.
Rational Exponents
Radical expressions can be rewritten using rational
(fractional) exponents. For example,
1
2
5 5
and
5
1
5
3 3
.
In general, for any real number
a
and any natural
numbers
m
and
n
with
1
n
1.
1
n
n
a
a
.
2.
)
(
m
m
n
m
n
n
a
a
a
3.
1
1
m
n
m
m
n
n
a
a
a
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentMath 1513 Sec R.7
2
These properties, along with the properties of radicals
and the properties of exponents we talked about earlier,
allow us to work many types of problems involving
radicals.
Examples:
a.
Simplify:
3
x x
1
1
3
2
1 1
2 3
3
2
6 6
5
6
5
6
3
x x
x x
x
x
x
x
b.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 staff
 Algebra, Radicals, Exponents, Pythagorean Theorem, 1513 Sec

Click to edit the document details