1. Multiplying and Dividing Radical Expressions

2. Multiplying
If there are two radicals being multiplied and they have the same root then the radicands are multiplied
Always check to see if the radicals can be simplified before multiplying!

3. Dividing
If there are two radicals with the same root being divided then they can be combined under a single radical and the radicands can be divided
If the two radicands do not divide evenly then we must rationalize our denominator…

4. Rationalizing the Denominator
Rewrite it so there are no radicals in any denominator and no denominators in any radicals
Multiply the denominator by something to make it a perfect root

5. Examples! 

6. Binominal radical expressions

7. Adding and Subtracting Expressions
1st: Simplify all expressions
Then combine like terms
If radicals have difference indexes then they are NOT like terms
If the radicands are different then they are NOT like terms

8. Multiplying Expressions
Use FOIL for binominals and distribution for all others
Both the coefficients and the radicands are multiplied
After multiplication all radicals should be simplified

9. Dividing Expressions (Rationalize Denominator)
When dividing…
Remember that no radicals can exist in denominators so they should be rationalized.
If we have a binominal, to rationalize we change the sign of the radical and multiply by it over itself.

10. Examples! 