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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:

Solution

To simplify, use the Division Property of Radicals to rewrite each radical.

a.  
  Write each radical as a quotient of radicals.
  Simplify
b.  
  Write each radical as a quotient of radicals.
  Simplify

 

 
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