Combining Like Radical Terms
Adding and subtracting radical expressions is like adding and subtracting
polynomials.
â€¢ With polynomials, to add like
terms, we add their coefficients. 
2x + 3x = (2 + 3)x = 5x 
â€¢ 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, 

