Radicals Packet Worksheet Page 2
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6Rationalizing and Dividing Radicals
When working with radicals, a radical cannot be in the denominator. When left with a radical
in the denominator, the expression must be rationalized. Multiply the top and bottom of the
fraction by what is needed, not solely by what’s in the radical. This will come into play when
dividing radicals. When faced with a binomial in the denominator, the top and bottom must
be multiplied by the conjugate.
Rationalize the denominator of each of the following.
1
5
8
3
A)
B)
C)
D)
5
3
2
3
10
12
12x y
5
10
4
3
E)
F)
G)
H)
2
3
6 2
4
8
5
7
3
5
3
15x y z
16x y
12x y
30
12
20
I)
J)
K)
+
−
−
7
2
5
6
3 2 4
Addition/Subtraction with Radicals
Simplify each of the following.
+
−
+
+
A) 6 3 7 3
B) 4 2 9 2 6 2
C)
12
27
−
+
−
+
−
3
3
D) 9 48 3 27 12 147
E) 13 90 4 40 7 250
F)
12 24 6 81
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