CHAPTER 3 Section 3.3: Add and Subtract Radical Expressions
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Section 3.3: Add and Subtract
Radical Expressions
Objective: Add and subtract like radicals by first simplifying each radical.
Adding and subtracting radical expressions is very similar to adding and subtracting
variable expressions. If two or more radical expressions have the same indices and the same
radicands, they are called like radicals. Consider the similarities between the following two
examples.
Example 1. Perform the indicated operations.
5 3 2x x x
Combine like terms
6x
Our Answer
Example 2. Perform the indicated operations.
5 11 3 11 2 11
Combine like radicals
6 11
Our Answer
Notice that when we combined the radical terms with
11
it was just like combining
variable terms with
.x
When adding and subtracting like radicals, we add and subtract the
coefficients in front of the radical, and the radical stays the same.
Example 3. Perform the indicated operations.
5 5 5 5
7 6 4 3 9 3 6
Combine like radicals
55
7 6 6
and
55
4 3 9 3
55
8 6 5 3
Our Answer
We cannot combine these radical expressions any more because the radicals are not like
radical terms.
Often radical expressions do not look like at first. However, if we simplify the radicals, we
may find we do in fact have like radicals. This process is shown in the examples on the
next page.
