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:
We multiply the radicands.
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:
Multiply 8w by 5y. Multiply 7y by 4x.
Simplify.
In the following multiplication problem, we use the Distributive Property
to remove the parentheses.
Find this product:
Distribute
to each term
inside the parentheses.
Simplify.
Example 1
Multiply and simplify:
Solution
Distribute
Multiply.
Factor each radicand.
Use perfect square
factors when possible.
Write each radical as a
product of radicals. Place
each perfect square under
its own radical symbol.
to each term
inside the parentheses.
