Algebra Demystified 2nd Ed

120 algebra De mystif ieD

DeMYSTiFieD / algebra DeMYSTiFieD / HuttenMuller / 000-0 / Chapter 5

✔SOLUTIONS

1.^3
5

3

5

5

5

35

5

35

(^25)
=⋅==

2.^77772
yy

y

y

y

y

y

y

=⋅==

3.^6
7

6

7

7

7

42

7

42

(^27)
=⋅==

4.^8
3

8

3

3

3

83

3

83

(^23)
xx=⋅==xx

5.^7
11

7

11

11

11

77

11

77

(^211)
xy=⋅xy ==xy xy

6.^2
10

2

10

10

10

210

10

210

yy^210

y

y

y

y

y

y

=⋅==

()

In the case of a cube (or higher) root, multiplying the fraction by the denom-

inator over itself usually does not work. To eliminate the nth root in the

denominator, we need to write the denominator as the nth root of some quan-

tity to the nth power. For example, to simplify^1

(^35)
we need 5^3 under the radical.
To get 53 under the radical, we multiply the numerator and denominator by^352
over itself. Thus,
1
5
5
5
5
5
25
(^35)
3 2
3 2
3 2
3 3
3
⋅==
When the denominator is written as a power (often the power is 1) subtract
this power from the root. The factor will include this number as an exponent.
EXAMPLES
Rationalize the denominator.
(^483)
x
EXAMPLES
Rationalize the denominator.
EXAMPLES
Rationalize the denominator.