document.write( "Question 683345: Simplify the radical expression: radical sign -8x^3? What steps do I take to simplify the expression? \n" ); document.write( "

Algebra.Com's Answer #423521 by fcabanski(1391) $\"\"$ $\"About$

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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.

\n" ); document.write( " $\"sqrt%28-8x%5E3%29+=+sqrt%28-1%2A2%2A2%2A2%2Ax%2Ax%2Ax%29\"$

\n" ); document.write( "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.

\n" ); document.write( " $\"2x%2Asqrt%28-2x%29\"$ 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 $\"2xi%2Asqrt%282x%29\"$

\n" ); document.write( "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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