Properties Of Radicals, Simplifying Radicals, Rationalizing Operations Worksheet - Section A-7 Page 4
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9A-60
Appendix A A BASIC ALGEBRA REVIEW
useful is a simplified form. An algebraic expression that contains radicals is said
to be in simplified form if all four of the conditions listed in the following def-
inition are satisfied.
SIMPLIFIED (RADICAL) FORM
D E F I N I T I O N
1. No radicand (the expression within the radical sign) contains a factor
to a power greater than or equal to the index of the radical.
2
5
For example,
x
violates this condition.
2. No power of the radicand and the index of the radical have a com-
mon factor other than 1.
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4
For example,
x
violates this condition.
3. No radical appears in a denominator.
For example,
y/ x
violates this condition.
4. No fraction appears within a radical.
3
For example,
violates this condition.
5
E X A M P L E
Finding Simplified Form
3
Express radicals in simplified form.
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5
2
2
4
2
Condition 1 is not met.
(A)
12x
y
z
(4x
y
z
)(3xy)
pm
pn
m
n
p
2
2
x
y
(x
y
)
(2xy
z)
(3xy)
n
n
n
2
2
xy
x
y
(2xy
z)
3xy
n
2
n
x
x
2xy
z
3xy
3
3
3
n
n
n
2
5
2
2
5
2
(B)
6x
y
4x
y
(6x
y)(4x
y
)
x
y
xy
3
7
3
24x
y
3
6
3
Condition 1 is not met.
(8x
y
)(3x)
3
pm
pn
m
n
p
2
3
x
y
(x
y
)
(2x
y)
(3x)
3
3 3
n
n
n
2
xy
x
y
(2x
y)
3x
3
n
2
n
x
x
2x
y
3x
6
4
2
2
2
1/6
Condition 2 is not met.
(C)
16x
y
[(4x
y)
]
2
2/6
(4x
y)
Note the convenience of using rational
exponents.
2
1/3
(4x
y)
3
2
4x
y
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