document.write( "Question 623092: simplify
\n" ); document.write( "root symbol 39a^3b^5/root symbol 13a2b
\n" ); document.write( "I am having difficulty with this can you help please???? \n" ); document.write( "
Algebra.Com's Answer #391890 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
I assume by \"root symbol\" you mean square root. (In the future, please specify which kind of root.) I also assume that \"13a2b\" means \"13a%5E2%2Ab\"

\n" ); document.write( "There are several ways to deal with a fraction of square roots. My prefernce is to do the following:
  1. Use the \"root%28a%2C+p%29%2Froot%28a%2C+q%29+=+root%28a%2C+p%2Fq+%29\" property to join the two square roots into one.
  2. Reduce the fraction. (Note: If you're clever you will keep in mind step 3 and maybe not reduce the fraction as fully as possible. For example, if you had \"sqrt%282%2F4%29\" then you would not reduce the fraction because step 3 wants perfect square denominators. 4 is already a perfect square. If we reduce 2/4 to 1/2 then we would no longer have a perfect square denominator. And we would end up changing 1/2 back to 2/4 in step 3.)
  3. If there still is a denominator, then make sure it is a perfect square.
  4. If there still is a denominator, then use the \"sqrt%28p%29%2Fsqrt%28q%29+=+sqrt%28p%2Fq%29\" property again, this time in the other direction -- to split the numerator from the denominator.
  5. Simplify any remaining square roots and fractions.
Let's see this in action:
\n" ); document.write( "\"sqrt%2839a%5E3b%5E5%29%2Fsqrt%2813a%5E2%2Ab%29\"
\n" ); document.write( "1. Join the square roots:
\n" ); document.write( "\"sqrt%28%2839a%5E3b%5E5%29%2F%2813a%5E2%2Ab%29%29\"
\n" ); document.write( "2. Reduce the fraction (maybe not fully).
\n" ); document.write( "The entire denominator cancels out leaving:
\n" ); document.write( "\"sqrt%28%283ab%5E4%29%2F1%29\"
\n" ); document.write( "or just
\n" ); document.write( "\"sqrt%283ab%5E4%29\"
\n" ); document.write( "3. If there's a still denominator, ...
\n" ); document.write( "There is no denominator.
\n" ); document.write( "4. If there's a still denominator, ...
\n" ); document.write( "There is no denominator.
\n" ); document.write( "5. Simplify any remaining square roots and fractions.
\n" ); document.write( "To simplify a square root, look for perfect square factors of the radicand (the expression inside). There are not prefect square factors in the 3 or the a. But there are perfect square factors in \"b%5E4\". When I factor out the perfect squares I like to put those factors in front:
\n" ); document.write( "\"sqrt%28b%5E2%2Ab%5E2%2A3a%29\"
\n" ); document.write( "Then you use another property of radicals, \"root%28a%2C+p%2Aq%29+=+root%28a%2C+p%29%2Aroot%28a%2C+q%29\", split the square root so that eah perfect square factor is in its own square root:
\n" ); document.write( "\"sqrt%28b%5E2%29%2Asqrt%28b%5E2%29%2Asqrt%283a%29\"
\n" ); document.write( "The square roots of the perfect squares simplify:
\n" ); document.write( "\"b%2Ab%2Asqrt%283a%29\"
\n" ); document.write( "which simplifies to:
\n" ); document.write( "\"b%5E2%2Asqrt%283a%29\" \n" ); document.write( "
\n" );