Practice Page

Math A

Addition and Subtraction of Radicals 


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 them.  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.
 

 

Let's try one together.

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:

 

 

Let's try another one:

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

 

 


Caldwell