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