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, letâ€™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, letâ€™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.


Simplify each radical.


Thus, 

