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Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

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Lesson Transcript

Instructor:
*Jennifer Beddoe*

Multiplying 2 or more radical expressions uses the same principles as multiplying polynomials, with a few extra rules for dealing with the radicals. This lesson will teach you how to multiply and then simplify radical expressions.

When multiplying expressions that contain radicals, it can be most helpful to remember the product rule for radicals. This rule states that if you have two terms that contain radicals, you can combine them under the same radical symbol if the index is the same. The **index** of a radical is the superscript number in the 'V' part of the radical.

This radical has an index of 3 and it is called the cube root. If there is no number there, the index is assumed to be 2. That is referred to as the square root. Cube roots and square roots are the most common radicals.

Here is an example of how the product rule for radicals works.

You can see that by combining the terms under the radicals, the multiplication problem looks much easier to solve.

By using the product rule to combine terms under the same radical symbol, it's easy to take the next step and multiply those terms together. In our previous example, we can quickly see that we need to multiply 5 and 3, which is 15. So the final answer to the problem is the square root of 15.

When multiplying 2 or more radical expressions, as long as each term has the same index, you can combine the terms under each radical and then multiply using the multiplication rule for exponents, which is that when terms have the same base, just add the exponents in order to multiply.

Let's try an example.

Multiply:

Since the index of each term is 4, you can combine each term under one radical symbol because of the product rule.

Then you can multiply each term together to get the answer:

The final step when working with all math problems is to make sure that your answer is in its simplest form. When dealing with radicals, this means that we need to remove whatever we can from under the radical symbol.

One thing that might make it easier to see what can come out from under the radical is to use the product rule in reverse. Let's finish the example problem from earlier.

The first step is to separate the terms:

When we do this, we see that the *y*^4 term can be reduced because the radical has the index of 4. They cancel each other out, and the term is simplified to *y*.

None of the other terms can be simplified, so the final answer to our question is:

Let's try one more example.

First, use the product rule to bring the terms under the same radical symbol.

Then, combine like terms:

Next, separate each term in order to simplify.

There are three terms that can be simplified.

Once you have simplified everything, you can combine the terms again to get your final answer:

To multiply radical expressions, use the product rule to collect all terms under the same radical. Remember, this will only work if the radicals have the same index. Then, combine like terms according to the rules of multiplication. Finally, simplify where possible.

Once you are finished with this lesson, you should be able to use the product rule to multiply radical expressions.

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Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

- How to Find the Square Root of a Number 5:42
- Estimating Square Roots 5:10
- Simplifying Square Roots When not a Perfect Square 4:45
- Simplifying Expressions Containing Square Roots 7:03
- Division and Reciprocals of Radical Expressions 5:53
- Radicands and Radical Expressions 4:29
- Evaluating Square Roots of Perfect Squares 5:12
- Factoring Radical Expressions 4:45
- Simplifying Square Roots of Powers in Radical Expressions 3:51
- Multiplying then Simplifying Radical Expressions 3:57
- Simplify Square Roots of Quotients 4:49
- Rationalizing Denominators in Radical Expressions 7:01
- Addition and Subtraction Using Radical Notation 3:08
- Multiplying Radical Expressions with Two or More Terms 6:35
- Solving Radical Equations: Steps and Examples 6:48
- Solving Radical Equations with Two Radical Terms 6:00
- Go to High School Algebra: Radical Expressions

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