Multiplication Property of Radicals
The Multiplication Property of Radicals allows us to write a single radical
as the product of two radicals.
Here are two examples: 
Square Root

Cube Root

The property can also be used to write the product of two radicals as a
single radical, provided the two radicals have the same index.
Here are two examples: 
Square Root

Cube Root

Property â€”
Multiplication Property of Radicals
English The n^{th} root of a product is the product of the n^{th} roots.
Algebra
where
and
are real numbers and n is a positive
integer.
Example
Note:
If x is negative, then
For example, if x = 3:
In the remainder of this Topic, we will assume that each variable under a
radical represents a nonnegative real number.
Example
Simplify:
a.
b.
Solution
To simplify, use the Multiplication Property of Radicals to rewrite each
radical.
Note:
If possible, write the radicand as a product
where one exponent is a multiple of the
index. Use the largest multiple possible.
Here are three examples:
