document.write( "Question 29083: im having trouble figureing out these sorts of problems ive donw really good in math up until algebra 2 and now im stuck how do you take the 3rd root of -125 \n" ); document.write( "

Algebra.Com's Answer #15882 by Earlsdon(6294) $\"\"$ $\"About$

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\n" ); document.write( " $\"%28-125%29%5E%281%2F3%29\"$ So you are really looking for a number n, such that $\"n%5E3+=+-125\"$
\n" ); document.write( "You try can factoring -125. But you want the factors to be identical, so start with +125.
\n" ); document.write( "You know 125 divides by 5 because its one's position is 5, so:
\n" ); document.write( "5(25) = 125 Now factor the 25 to get 5*5.
\n" ); document.write( "So, now you have 5*5*5 = 125 A good start, but you really want to get -125, try (-5)(-5)(-5) = -125 Aha! So:
\n" ); document.write( " $\"%28-125%29%5E%281%2F3%29+=+%28%28-5%29%28-5%29%28-5%29%29%5E%281%2F3%29\"$ = $\"%28%28-5%29%5E3%29%5E%281%2F3%29\"$ = -5\r
\n" ); document.write( "\n" ); document.write( "The third root of -125 = -5
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