1. Simplifying nth Roots
There is a very important form for simplifying radicals.
When the index and the exponent are the same value, the result is base b.
There is an exception in using this rule, and it will be discussed later.

2. Example 1

3. Example 2
Example 3

4. The exception to the rule occurs when both of the following apply:
n is even
b is negative

5. Example 4
Note that we have an exception since:
n is even
b is negative

6. Simplifying without using the new rule …
Consider how the answer …
… compares with the original value of b.
Answer
= absolute value of b.

7. This suggests a new rule when the exception conditions are met:
When both statements are true…
n is even
b is negative
… evaluate as follows:

8. SUMMARY
Odd
Positive or
Negative
Even

9. Example 5
Exception?
n = 4 is even
b = - 5 is negative

10. Example 6
Exception?
n = 3 is odd
no exception

11. Exception? Example 7 n = 4 is even
b = 2x could be negative if x was negative
Since its only the x that can be negative, we can also write …

12. END OF PRESENTATION