SOLUTION: Simplify the radical: radical sign -8x^3........what does it means to simplify and how do you go by simplifying?

Algebra ->  Radicals -> SOLUTION: Simplify the radical: radical sign -8x^3........what does it means to simplify and how do you go by simplifying?      Log On


   

Question 683341: Simplify the radical: radical sign -8x^3........what does it means to simplify and how do you go by simplifying?
Found 2 solutions by fcabanski, josmiceli:
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.

Hope the solution helped. Sometimes you need more than a solution. Contact fcabanski@hotmail.com for online, private tutoring, or personalized problem solving (quick for groups of problems.)


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Is this it:
+sqrt%28+-8%2Ax%5E3+%29+ ? If so:
You can break it up like this:
+sqrt%28+-8%2Ax%5E3+%29+=+sqrt%28+-1%2A8%2Ax%5E3+%29+
+sqrt%28-1%29+%2A+sqrt%288%29+%2A+sqrt%28+x%5E3+%29+
+i+%2A+2%2Asqrt%282%29+%2A+sqrt%28x%5E3%29+
+2%2Asqrt%28+2x%5E3+%29%2Ai+
This is only slightly better, so you're
right- it isn't much of a simplification.