To simplify nth roots, the radicand must have no perfect nth power factors. This can be done through prime factorization or taking out the largest perfect root factor. Practice problems are provided to simplify nth roots with numbers, variables, and combinations using these methods so the exponent of any variable in the radicand and the index of the radical have a greatest common factor of one.

1. SIMPLIFYING
NTH ROOTS

2. CONDITION FOR SIMPLIFIED NTH
ROOTS
A radical expression is not considered
simplified until the radicand has no
perfect nth power factors.

3. METHODS TO SIMPLIFY NTH
ROOTS
 Prime Factorization
 Example:
 Largest Perfect Root Factor
 Example:

4. Take out your Exponent Table to
help with Simplifying!! 
Use your TI-84

5. PRACTICE!
Simplify Nth Roots (numbers only)

11. CONDITION FOR SIMPLIFIED NTH
ROOTS
A radical expression is not considered
simplified unless the exponent of any
variable in the radicand and the index of
the radical have a GCF of one.

12. PRACTICE!
Simplify Nth Roots (variables only & combo)