In this video, we will multiply radical expressions. After you finish this lesson, view all of our Algebra 1 lessons and practice problems.

Let’s start with simple expressions.

In other words,

Let’s try other examples:

would equal to

would equal to , which is a perfect square so it would be

Let’s try the same problem by using another method:

would equal to can also be written as

This also leads to the answer of 6

For , it would equal to

*25* goes into *675* twenty-seven times

Since *5* is the square root of *25*, can be written as

This can be further simplified into

## Examples of Multiplying Radical Expressions

### Example 1

Use the rule to multiply the radicands

Look for perfect squares in the radicand, and rewrite the radicand as the product of two factors.

Simplify,

### Example 2

Use the rule to multiply the radicands

Simplify,

## Video-Lesson Transcript

Let’s go over how to multiply radical expressions.

First, let’s start with

So if you look, closely

Keep this in mind as we move forward in the lesson.

Let’s take a look at this

this cannot be simplified.

But what if we reduce this first?

So you can multiply it across and get an answer.

Or reduce it first and multiply it out.

Let’s have this one

I can multiply this out

Then we should break down.

But it’s a pretty large number.

Let’s see what happens if we simplify the radical expressions first.

We came up with the same answer.

The number of steps in the two methods is pretty much the same.

But I dealt with smaller numbers using the second method.

Let’s look back at a point here.

At this point, we know that can’t be broken down.

But there’s a there.

And we know that goes into .

So, we might as well break it down. So we’ll have

Let’s just reorganize this

And we’ll solve