SOLUTION: Simplify the radical expression: radical sign -8x^3? What steps do I take to simplify the expression?

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Question 683345: Simplify the radical expression: radical sign -8x^3? What steps do I take to simplify the expression?
Answer by fcabanski(1391) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify means pull out all square factors (for square root) if it's cube root pull out all cube factors. I'll proceed as if it's square root.


sqrt%28-8x%5E3%29+=+sqrt%28-1%2A2%2A2%2A2%2Ax%2Ax%2Ax%29


Remove anything that appears twice. Outside the radical it is just one factor. So remove 2*2 and x*x. Outside the radical those are 2x which leaves -1*2*x or -2x inside the radical.


2x%2Asqrt%28-2x%29 But for square root there can't be a negative number inside the radical. The square root of -1 is the imaginary number i. So this becomes 2xi%2Asqrt%282x%29


If the problem is a cuberoot cbrt%28-8x%5E3%29 then pull out anything that's shown three times, and the factor is negative because -*-*- = -. So the answer would be -2x.

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