Radical Expressions

**Learning Objectives**

After completing this tutorial, you should be able to:

- Add and subtract like radicals.
- Multiply radical expressions.

** Introduction**

In this tutorial we will look at adding, subtracting and multiplying
radical expressions. If you
need a review on what radicals are, feel free to go to **Tutorial
37: Radicals**. If it is simplifying radical expressions that
you need a refresher on, go to **Tutorial
39: Simplifying Radical Expressions**. Ok, I think you are
ready to begin this tutorial.

** Tutorial**

The following are two examples of two different pairs of like radicals:

**Adding and Subtracting **

**Radical Expressions**

If you need a review on simplifying radicals go to **Tutorial
39: Simplifying Radical Expressions.**

You can only add or subtract radicals together if they are **like
radicals. **

You add or subtract them in the same fashion that you do like terms
shown in **Tutorial 25: Polynomials
and Polynomial Functions**. Combine the numbers that are in front
of the like radicals and write that number in front of the like radical
part.

The 20 in the first radical has a factor that we can take the square
root of.

Can you think of what that factor is?

**Let's see what we get when we simplify the first radical:**

The 24 in the second radical has a factor that we can take the cube
root of.

Can you think of what that factor is?

**Let's see what we get when we simplify the second radical:**

***Cube root of 8 is 2**

We can take the cube root of the *b* cubed
in the third radical and 81 has a factor that we can take the cube root
of.

Can you think of what that factor is?

**Let's see what we get when we simplify the third radical:**

***Cube root of 27 b cubed is 3b**

***Combine like radicals**

We can take the fourth root of the 16 in the first radical:

***Fourth root of 16 is 2**

***Combine like radicals**

**Multiplying Radical Expressions**

Follow the **multiplication
property of radicals found in Tutorial 39: Simplifying Radical Expressions** and the same basic properties used to **multiply
polynomials together found in Tutorial 26: Multiplying Polynomials ** to multiply radical expressions together.

**AND**

**Step 2: Simplify
the radicals.**

**AND**

**Step 2: Simplify
the radicals.**

**AND**

**Step 2: Simplify
the radicals.**

** Practice Problems**

These are practice problems to help bring you to the
next level.
It will allow you to check and see if you have an understanding of
these
types of problems. **Math works just like
anything
else, if you want to get good at it, then you need to practice
it.
Even the best athletes and musicians had help along the way and lots of
practice, practice, practice, to get good at their sport or instrument.**
In fact there is no such thing as too much practice.

To get the most out of these, **you should work the
problem out on
your own and then check your answer by clicking on the link for the
answer/discussion
for that problem**. At the link you will find the answer
as well as any steps that went into finding that answer.

Practice Problems 1a - 1b:Add or subtract.

Practice Problems 2a - 2b:Multiply and simplify.

** Need Extra Help on these Topics?**

**Go to Get
Help Outside the
Classroom found in Tutorial 1: How to Succeed in a Math Class for
some
more suggestions.**

Last revised on July 21, 2011 by Kim Seward.

All contents copyright (C) 2001 - 2011, WTAMU and Kim Seward. All rights reserved.