Simplifying nth Roots
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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 3


n is even

b is negative


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:



Exception?

n = 4 is even

b= - 5 is negative


Exception?

n = 3 is odd

no exception


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 …



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