Multiplying Radical Expressions
We can multiply radicals provided they have the same index. To multiply
the radicals, we multiply their radicands. The resulting radical has the
common index.
| For example, let’s find this product:
|
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| We multiply the radicands.
|
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| Finally, we simplify. |
= 2 |
If the expressions being multiplied contain factors that are not under a
radical symbol, multiply those factors. Then multiply the radicands of
radicals that have the same index.
| For example, let’s find this product:
|
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| Multiply 8w by 5y. Multiply 7y by 4x.
|
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| Simplify. |
 |
In the following multiplication problem, we use the Distributive Property
to remove the parentheses.
| Find this product:
|
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Distribute
 to each term
inside the parentheses.
|
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| Simplify. |
 |
Example 1
Multiply and simplify:
| Solution |
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Distribute
 |
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| Multiply. |
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| Factor each radicand.
Use perfect square
factors when possible. |
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| Write each radical as a
product of radicals. Place
each perfect square under
its own radical symbol.
|
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| Simplify each radical.
|
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| Thus, |
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| 
