document.write( "Question 352886: How do I simplify 3√(-1/125)? \n" ); document.write( "

Algebra.Com's Answer #252317 by jsmallt9(3758) $\"\"$ $\"About$

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$\"3sqrt%28-1%2F125%29\"$
\n" ); document.write( "With a negative radicand (expression with a radical), this expression is going to be an imaginary number. And with imaginary numbers we use i to factor out the factor of -1:
\n" ); document.write( " $\"3sqrt%28-1%2A%281%2F125%29%29\"$
\n" ); document.write( " $\"3sqrt%28-1%29sqrt%281%2F125%29\"$
\n" ); document.write( " $\"3i%2Asqrt%281%2F125%29\"$
\n" ); document.write( "Next, a simplified radical expression has ...
\n" ); document.write( "- No radicals in a denominator
\n" ); document.write( "- No fractions in a radicand
\n" ); document.write( "We have a fraction in the radicand so we have more work to do. Although there are other ways to simplify radicands with fractions, I like to start by making the denominator a perfect square. So we'll start by figuring out what we can multiply 125 by to turn it into a perfect square. Surely multiplying by 125 will work. But there is a smaller number that will work. And since smaller numbers are easier to work with, I prefer to go that way. Since $\"125+=+5%2A5%5E2\"$ I can see that just another factor of 5 will make 125 a perfect square, It will be the perfect square of 5*5 or 25:
\n" ); document.write( " $\"3i%2Asqrt%28%281%2F125%29%285%2F5%29%29\"$
\n" ); document.write( " $\"3i%2Asqrt%285%2F625%29\"$
\n" ); document.write( "Now we'll split the fraction into spearate square roots:
\n" ); document.write( " $\"3i%2Asqrt%285%29%2Fsqrt%28625%29\"$
\n" ); document.write( "and replace $\"sqrt%28625%29\"$ with 25:
\n" ); document.write( " $\"3i%2Asqrt%285%29%2F25\"$
\n" ); document.write( "This is our simplified expression. An alternate form, which may be preferred by your teacher, would be:
\n" ); document.write( " $\"%283sqrt%285%29%2F25%29i\"$
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