Question 683341
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.<P>
{{{sqrt(-8x^3) = sqrt(-1*2*2*2*x*x*x)}}}<P>
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.<P>
{{{2x*sqrt(-2x)}}}  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*sqrt(2x)}}}<P>
If the problem is a cuberoot {{{cbrt(-8x^3)}}} then pull out anything that's shown three times, and the factor is negative because -*-*- = -.  So the answer would be -2x.
<P>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.)