Algebra Worksheets - Complete Set With Answers Page 53
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72SIMPLIFYING RADICALS WITH VARIABLES - 8.2
In a square root the index is 2
2
x
In a cube root the index is 3
3
x
In a fourth root the index is 4
4
x
To simplify radicals with variables look at the radical as a “jail” with the variables trying to “break
out”. The index indicates how many must be in a group to "break out". For instance, if the index is 3
then there must be 3 of the same thing to escape.
3
3
3
x
=
x x x = x
4
4
x
=
= x
3
3
6
2
Take note of this one:
x
=
x x x x x x = x
(Notice the square means two groups).
But, watch what happens when there is an extra variable……..
2
5
5
2
x
(which really means
x
) =
x x x x x = x
x
To figure the answer without drawing all the x’s, simply divide the index into the exponent. The number of
times the answer comes out evenly, is the exponent of the variable on the outside and the remainder is the
exponent under the radical in the answer.
7
4
7
3
x
(
= 3 remainder 1) = x
x
3
3
4
x
(
= 1 remainder 1) = x
x
2
3
16
14
16
8
x
(
= 8, no remainder) = x
4
4
14
3
2
x
(
= 3, remainder 2) = x
x
2
4
Try these:
3
4
3
5
9
7
13
20
17
1.
x
____ 2.
x
____
3.
x
____ 4.
x
____
5.
x
____
6.
x
____
49
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