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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. Example 1. Example 2. Example 3.
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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.
Example 2 • Example 3
The exception to the rule occurs when both of the following apply: n is even b is negative
Example 4 Note that we have an exception since: n is even b is negative
Simplifying without using the new rule … Consider how the answer … … compares with the original value of b. Answer = absolute value of b.
n is even b is negative This suggests a new rule when the exception conditions are met: Exception When both statements are true… … evaluate as follows:
Example 5 Exception? n = 4 is even b= - 5 is negative
Example 6 Exception? n = 3 is odd no exception
Example 7 Exception? n = 4 is even b= 2xcould be negative if x was negative Since its only the x that can be negative, we can also write …
