1.06 Radicals
and Fractional Exponents
Rationalizing Monomial
Denominators
College Algebra: One Step at a Time,
Page
77-79: #13, 17, 21, 23, 25, 27.
Dr. Robert J. Rapalje
Seminole Community College
Sanford, FL 32773
13.
Notice
that the denominator has a cube root that is not a perfect cube! The goal,
in rationalizing the denominator, is to get a perfect cube for the
denominator. In this case, it would be nice to get a denominator like
.
To do this, you need to multiply numerator and denominator by
.
It looks like this:
Divide out
the factor of 3:
As a
check, calculate the value of the problem: =
4.160167646
then
calculate the value of your answer :
=
4.160167646
17.
Notice
that the denominator has a cube root that is not a perfect cube! The
denominator does factor into 
. The goal, in rationalizing the denominator, is to get a
perfect cube for the denominator. In this case, it would be nice to get a
denominator like
. To do this, you need to multiply numerator and
denominator by 
. It looks like this:
Divide out
the factor of 7:
As a
check, calculate the value of the problem:
= 9.564655914
then
calculate the value of your answer : = 9.564655914
21.
Notice that the denominator has a cube root that is not a perfect cube! The
denominator does contain 4 which is
.
The goal, in rationalizing the denominator, is to get a perfect cube for the
denominator. In this case, it would be nice to get a denominator like
.
Since you already have 
,
to get the
,
you need to multiply numerator and denominator by
.
As to the variables 
,
for perfect cubes, it is necessary to get exponents that are divisible by 3,
such as 
.
Since you already have the 
,
to get the 
,
you will need to multiply numerator and denominator by
.
Altogether, it looks like this:
The denominator is (of
course!) a perfect cube, so you can simplify this:
The
fraction reduces, so divide out the
.
23.
Notice that the denominator has a cube root that is not a perfect cube! The
denominator does contains 25 which is
.
The goal, in rationalizing the denominator, is to get a perfect cube for the
denominator. In this case, it would be nice to get a denominator like
.
Since you already have
,
to get the
,
you need to multiply numerator and denominator by
.
As to the variables
,
for perfect cubes, it is necessary to get exponents that are divisible by 3,
such as 
.
Since you already have the 
,
to get the 
,
you will need to multiply numerator and denominator by . Altogether, it
looks like this:
The denominator is
(of course!) a perfect cube, so you can simplify this:
The
fraction reduces, so divide out the
.
25.
=
Notice that the denominator has a fifth root that is not a perfect fifth
power! The denominator contains 4 which is . The goal,
in rationalizing this denominator, is to get a perfect fifth power for the
denominator. In this case, it would be nice to get a denominator like
.
Since you already have
,
to get the
,
you need to multiply by
.
As to the variables
,
for perfect fifth powers, it is necessary to get exponents that are
divisible by 5, such as 
.
Since you already have the 
,
to get the 
,
you will need to multiply numerator and denominator by
.
Altogether, it looks like this:
The denominator is
(of course!) a perfect cube, so you can simplify this:
The
fraction reduces, so divide out the
.
27.
=
Notice that the denominator has a fifth root that is not a perfect fifth
power! The denominator contains 16 which is
.
The goal, in rationalizing this denominator, is to get a perfect fifth power
for the denominator. In this case, it would be nice to get a denominator
like.
Since you already have
,
to get the
,
you need to multiply numerator and denominator by
.
As to the variables
,
for perfect fifth powers, it is necessary to get exponents that are
divisible by 5, such as 
.
Since you already have the 
,
to get the 
,
you will need to multiply numerator and denominator by
.
Altogether, it looks like this:
The denominator is
(of course!) a perfect cube, so you can simplify this:
The
fraction reduces, so divide out the
.
Return to main page
Math in Living
C
O
L O
R
!!
Return to Basic Algebra page
Return to Intermediate Algebra page
Return to
College Algebra page
: View Source, Show