Multiplying Radicals
The product rule for radicals,
 allows multiplication of
radicals with the same index, such as
Caution
The product rule does not allow multiplication of radicals that
have different indices. We cannot use the product rule to multiply
Example 1
Multiplying radicals with the same index
Multiply and simplify the following expressions. Assume the variables represent
positive numbers.
Solution
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Product rule for radicals |
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Product rule for radicals |
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Simplify. |
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Product rule for radicals |
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Simplify |
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Rationalize the denominator. |
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We find a product such as
 by using the distributive property
as we do when multiplying a monomial and a binomial. A product such as
 can be found by using FOIL as we do for the product
of two binomials.
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