Luttrell 2012
108
Name: ______________________
Date: _____
7g – Combining Radicals
Adding
radicals is similar to adding like terms. Like terms are combined by adding the
coefficients. When radicals have the same radicands and root indices, then add the coefficients.
E
x
ample A:
2 3
4 3
6 3
+
=
E
x
ample B:
2 3
4 3
3
+
Example B cannot be simplified because the root indices are different.
Simplify e
x
actl
y
:
1.
−
+
3 24
2 54
2.
−
+
3 3
2 27
3.
5 3
48
+
4.
3 1
4
−
5.
2
0
3
4
x
x
−
6.
8
2 32
+
Multiplying radicals can onl
y
be done easil
y
with those of the same root inde
x
. If the root
indices are the same, multipl
y
the radicands. Those with differing indices will be dealt with
later.
E
x
ample C:
2 24
48
4 3
=
=
E
x
ample D:
(
)
(
)(
)
2 5
2 5 2 5
4 5
20
2
=
= ⋅ =
See a trick? Share it!___________________________________________________
Simplif
y
each e
x
pression:
7.
6 12
8.
2 8 4
9.
(
)
3 6
2
10.
(
)(
)
3 8 2 12
11.
3
8
2
(
)
−
12.
(
)
5 3
2
