Exponents And Radicals Worksheets Page 11
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15Simplest Radical Form
1.
All possible factors have been removed from the radical.
2.
All fractions have radical-free denominators.
3.
The index of the radical is reduced.
n
a b
is in simplest radical form if:
c
1. a/c is in simplest form;
2. c contains no radicals; and
3. b contains no perfect nth power factors.
Examples:
= 9x
⋅ 2 x = 3x 2x
3
2
18 x
a)
= 27a
⋅ 4 a
= 3a
3
7
6
3
6
6
2
2
3
3
108a
b
b
b
4 a
b)
c)
+ 2x 162x
4
5
4
32x
= 16x
⋅ 2x
+ 2x 81
⋅ 2x
4
4
4
4
4
( )
= 2x 2 x
+ 2x 3
4
4
2 x
(
)
= 1+ 3
4
2x 2 x
= 8x 2x
4
M161c1s2p2
11
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