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

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Simplifying nth roots

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.


Simplifying nth roots

  • Example 1


Simplifying nth roots

  • Example 2

  • Example 3


Simplifying nth roots

  • The exception to the rule occurs when both of the following apply:

n is even

b is negative


Simplifying nth roots

  • Example 4

Note that we have an exception since:

n is even

b is negative


Simplifying nth roots

Simplifying without using the new rule …

Consider how the answer …

… compares with the original value of b.

Answer

= absolute value of b.


Simplifying nth roots

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:


Simplifying nth roots

SUMMARY


Simplifying nth roots

  • Example 5

Exception?

n = 4 is even

b= - 5 is negative


Simplifying nth roots

  • Example 6

Exception?

n = 3 is odd

no exception


Simplifying nth roots

  • 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 …


Simplifying nth roots

END OF PRESENTATION


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