Operations with Radicals 

Simplification Addition and Subtraction Multiplication Division

Simplification of Radicals  Rule  Example  
Use the two laws of radicals to
SHORTCUT:



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Simplification Addition and Subtraction Multiplication Division 



Addition and Subtraction of radicals  Rule  Example  
Simplify all radicals. Combine only
like radical terms: Combine like radicals by combining the coefficients of the radical terms. The coefficient is the factor that sits outside the radical to the left. 
Note:

Example 1:
Example 2:


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Simplification Addition and Subtraction Multiplication Division 



Multiplication of radicals  Rule  Example  
If the indices are the same
NOTE: You may simplify the radicals before multiplying. However, you may need to simplify the radical again once you have found the product.

Example 1:
Example 2:


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Simplification Addition and Subtraction Multiplication Division 



Division  Rule  Example  
NOTE: A simplified radical contains no fractions and no radicals in the denominator.  
Division
Type I:



Division
Type II: 



(a + b) and (a  b) are conjugates: middle signs are opposite. Multiplying
by conjugates gives the difference of squares:




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Simplification Addition and Subtraction Multiplication Division 

