Division Property of Radicals
The Division Property of Radicals allows us to write a single radical as the
quotient of two radicals.
| Here are two examples: |
Square Root
 |
Cube Root
 |
It can also be used to write the quotient of two radicals as a single radical,
provided they have the same index.
| Here are two examples: |
Square Root
 |
Cube Root
 |
Property —
Division Property of Radicals
English The nth root of a quotient is the quotient of the nth roots.
Algebra
 where
 and
 are real numbers, b
≠ 0, and n is a
positive integer.
Example
Example
Simplify:
SolutionTo simplify, use the Division Property of Radicals to rewrite each radical.
| a. |
|
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| |
Write each radical as a quotient of radicals.
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| |
Simplify
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| b. |
|
 |
| |
Write each radical as a quotient of radicals.
|
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| |
Simplify
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