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 —
Multiplication Property of Radicals
English The nth root of a product is the product of the nth 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:
|
