In this video, we are going to be adding and subtracting radical expressions. After you finish this lesson, view all of our Algebra 1 lessons and practice problems.
We can add 
and we can do the same to 
Since we can only combine like terms, we know that we cannot add 
and 
together
so we cannot add 
and 
together either
For 
,
it would be 
Let’s look at other examples:
would stay like itself, while 
can be broken into 
Now that both expressions are like terms, they can be combined into 
After simplifying each radical expression, it will be 
After combining like terms, it will be 
Examples of Adding And Subtracting Radical Expressions
Example 1
First, let’s simplify all these radical expressions
Now, let’s combine the like terms.
Our answer is
Example 2
First, let’s simplify all these radical expressions
Now, let’s combine the like terms.
Our answer is
Video-Lesson Transcript
Adding and subtracting radical expressions.
Just like we could add
We could also add
Only like terms can be added.
Just like if we have
we cannot add them together.
We can also not add
it will just stay like this.
They won’t combine since they are different radicals.
So if we have
we can combine like terms, so the answer is
Let’s look at this one
This may look unlike terms so we can’t combine them.
But we can simplify this first.
The first expression can’t be simplified so we simplify the second expression.
Let’s simplify first.
I chose these because 
is a complete square.
Now, let’s our new expressions are
Since they are already like terms, we can combine them now.
So always make sure that they are in their simplest terms before we add them.
Because maybe they can be combined, they are not just in the correct format.
Let’s try this one now.
Let’s simplify all these first.
Now, let’s combine the like terms.
Our answer is
