SOLUTION: What is the principle of powers? Describe in your own words. When solving a radical equation, how do we use the principle of powers to eliminate radicals? Demonstrate with an examp

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Question 382642: What is the principle of powers? Describe in your own words. When solving a radical equation, how do we use the principle of powers to eliminate radicals? Demonstrate with an example. Make sure that it is your own example and significantly different from the examples already posted in the class discussion by your classmates.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
(I had to look this up because I wasn't familiar with the name)
Seems like the principle of powers says that if a = b, then a^n = b^n (however we must be careful when we take square, cubed, etc. roots, as I'll show later).
For example, we can solve sqrt%28x%2B2%29+=+7 by squaring both sides to obtain x%2B2+=+49 --> x = 47.
However, suppose we were given the equation x%5E4+=+1. Taking the fourth root of both sides it is easy to establish x = 1. It is correct, but there are three other values of x that satisfy: -1, i, and -i. These roots are often called "roots of unity."