SOLUTION: I am using the Power Principle to solve a radical equation. When I get to the point where I get (6-the square root of 6-2) squared, I know it factors out to be 36

SOLUTION: I am using the Power Principle to solve a radical equation. When I get to the point where I get (6-the square root of 6-2) squared, I know it factors out to be 36 - 12 square root

Question 784489: I am using the Power Principle to solve a radical equation. When I get to the point where I get (6-the square root of 6-2) squared, I know it factors out to be 36 - 12 square root of 6-x + 6 - x. My biggest question is, where does the 12 come from in front of the square root of 6-2?
Answer by xinxin(76) (Show Source): You can put this solution on YOUR website!
(6-the square root of 6-2) squared = (6-√6-2)*(6-√6-2)= 36 - 6√6 - 12 - 6√6 + 6 + 2√6 - 12 + 2√6 + 4 = 22 - 8√6
Since the terms under the square root symbol are the same, you can combine the coefficients in front of the square root symbol. You are not supposed to have x in the simplification step if the original equation does not have x. Pay attention to sign changes, when combine two minus signs you will get a plus sign.
If you were saying the equation was (6-the square root of(6-2))squared, you would get the integer 16 instead of the number above.

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