document.write( "Question 23815: Here is another one,\r
\n" ); document.write( "\n" ); document.write( "5/SQRT(8) \n" ); document.write( "
Algebra.Com's Answer #12571 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
  5\r\n" );
document.write( "————— \r\n" );
document.write( " Ö8\r\n" );
document.write( "\r\n" );
document.write( "The idea is to rationalize the denominator; that is get the\r\n" );
document.write( "denominator to be free of roots (radicals).  First we break \r\n" );
document.write( "8 into primes like this 2·2·2\r\n" );
document.write( "\r\n" );
document.write( "   5\r\n" );
document.write( "————————\r\n" );
document.write( " Ö2·2·2\r\n" );
document.write( "  \r\n" );
document.write( "Two of those 2's will pair up as 22 which will come out of the \r\n" );
document.write( "square root radical since it is a perfect square.\r\n" );
document.write( "\r\n" );
document.write( "   5\r\n" );
document.write( "————————\r\n" );
document.write( " Ö22·2\r\n" );
document.write( "  \r\n" );
document.write( "This will leave one 2 under the radical.  So we need another 2\r\n" );
document.write( "under that radical so it will pair with the other 2, so we will be able\r\n" );
document.write( "to take it out too.  To accomplish this we multiply numerator and \r\n" );
document.write( "denominator by Ö2\r\n" );
document.write( "      _\r\n" );
document.write( "   5·Ö2\r\n" );
document.write( "——————————\r\n" );
document.write( " Ö22·2·Ö2\r\n" );
document.write( "  \r\n" );
document.write( "Now we multiply under the radical on the bottom\r\n" );
document.write( "      _\r\n" );
document.write( "   5·Ö2\r\n" );
document.write( "—————————\r\n" );
document.write( " Ö22·2·2\r\n" );
document.write( " \r\n" );
document.write( "or \r\n" );
document.write( "\r\n" );
document.write( "     _\r\n" );
document.write( "  5·Ö2\r\n" );
document.write( "————————\r\n" );
document.write( " Ö22·22\r\n" );
document.write( "\r\n" );
document.write( "  \r\n" );
document.write( "Now we can take individual square roots on the bottom\r\n" );
document.write( "     _\r\n" );
document.write( "  5·Ö2\r\n" );
document.write( "—————————\r\n" );
document.write( " Ö22·Ö22\r\n" );
document.write( "\r\n" );
document.write( "and get 2·2\r\n" );
document.write( "      _\r\n" );
document.write( "   5·Ö2\r\n" );
document.write( "—————————\r\n" );
document.write( "   2·2\r\n" );
document.write( "  \r\n" );
document.write( "or\r\n" );
document.write( "\r\n" );
document.write( "   _\r\n" );
document.write( " 5Ö2\r\n" );
document.write( "—————\r\n" );
document.write( "  4\r\n" );
document.write( "\r\n" );
document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com
\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );