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3 Tutorials that teach Multiplying Radical Expressions

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Author: Sophia Tutorial
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This lesson shows how to multiply radical expressions.

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Tutorial

• Review of Distributive Rule and FOIL with Integers
• Review of Product Property of Radicals
• Multiplying Radical Expressions using Distribution and FOIL

Review of Distributive Rule and FOIL with Integers

The distributive rule allows us to distribute an outside factor into all terms of another factor.  For example:

If we have to factors in the form (a+b), we can use the distributive property in a different way, commonly referred to as the FOIL method.

FOIL: An acronym to remember the steps for distributing factors in binomial multiplication: first, outside, inside, last.

Let's see how the FOIL method can be used to multiply with integers:

Distribution and FOIL with Radical Expressions

The distributive rule and FOIL method can be applied to multiply expressions with radicals as well.  First, we will look at an example of distribution, where two identical radicals are multiplied together.

We can also use the FOIL method to distribute across two binomials in multiplication when there are radicals.  This is illustrated in the following example:

The distributive rule and the FOIL method can be applied to expressions containing radicals as well.  When two identical square roots are multiplied by each other, it evaluates to the expression underneath the square root.  This property also applies to other roots, such as cube roots, but the identical radical needs to be multiplied by itself 3 times, and so on.

Terms to Know
FOIL

An acronym to remember the steps for distributing factors in binomial multiplication: first, outside, inside, last.

Formulas to Know
FOIL Method