Addition and Subtraction
of Radicals
Topic Index | Algebra Index | Regents Exam Prep Center

(For this lesson, the term "radical" will refer only to "square root".)

When adding or subtracting radicals, you must use the same concept as that of adding or subtracting "like" variables. 
 
In other words, the radicals must be the same
before you add (or subtract) them.
 

Since the radicals are the same, simply add the numbers in front of the radicals (do NOT add the numbers under the radicals). 

 
Since the radicals are not the same, and both are in their simplest form, there is no way to combine these values.  The answer is the same as the problem.

Warning:  If the radicals in your problem are different, be sure to check to see if the radicals can be simplified.  Often times, when the radicals are simplified, they become the same radical and can then be added or subtracted.  Always simplify, if possible, before deciding upon your answer.
 

 
Example 1:

1.  Are the radicals the same? Answer:   NO
2.  Can we simplify either radical? Answer:  Yes,  can be simplified.
3.  Simplify the radical. Answer:
4.  Now, the radicals are the same
     and we can add.
Answer:

 

Example 2:

1. Simplify  Answer:
2. Simplify Answer:
3. Since the radicals in steps 1 and 2 are
    now the same, we can combine them.
Answer:  
4. After combining, you are left with: Answer:   
5. Can you combine these radicals? Answer:    NO
6. Therefore,

Answer:  

 

 


 
Topic Index | Algebra Index | Regents Exam Prep Center
Created by Michael Caldwell