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Combining Like Radical Terms

Adding and subtracting radical expressions is like adding and subtracting polynomials.

• With polynomials, to add like terms, we add their coefficients.

2x + 3x = (2 + 3)x = 5x

• With radical expressions, to add like radical terms, we add the numbers in front of the radicals.

Before we can combine radical terms, we sometimes need to simplify the individual radicals to obtain like terms.

Consider this example:
At first glance, we may think we cannot add the radical terms because the radicands are different.
However, if we simplify , we can combine like radical terms:

 

Example 2

Simplify:

Solution

First simplify

 The radicand, 75y, has a perfect square factor, 25.
Replace with
Combine the like radical terms,
Simplify.
So,

 

Example 3

Simplify:

Solution

First simplify

The radicand, 54x, has a perfect cube factor, 27.
Replace
Multiply
Combine the like radical terms
Simplify.
So,

 

 
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