document.write( "Question 38161: 
add and/or subtract and simplify the following radical expression. \r\n" );
document.write( "  __     __     __\r\n" );
document.write( "3Ö48 - 2Ö27 - 3Ö12\r\n" );
document.write( "\r\n" );
document.write( "thanks for your time
\n" ); document.write( "
Algebra.Com's Answer #23648 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
add and/or subtract and simplify the following radical expression. \r\n" );
document.write( "  __     __     __\r\n" );
document.write( "3Ö48 - 2Ö27 - 3Ö12\r\n" );
document.write( "\r\n" );
document.write( "thanks for your time\r\n" );
document.write( "  __     __     __\r\n" );
document.write( "3Ö48 - 2Ö27 - 3Ö12\r\n" );
document.write( "\r\n" );
document.write( "Break 48 down into primes: 48 = 8·6 = 4·2·2·3 = 2·2·2·2·3\r\n" );
document.write( "\r\n" );
document.write( "Break 27 down into primes: 27 = 3·9 = 3·3·3\r\n" );
document.write( "\r\n" );
document.write( "Break 12 down into primes: 12 = 4·3 = 2·2·3\r\n" );
document.write( "\r\n" );
document.write( "Replace the radicands by their prime factorizations:\r\n" );
document.write( "  _________     _____     _____\r\n" );
document.write( "3Ö2·2·2·2·3 - 2Ö3·3·3 - 3Ö2·2·3\r\n" );
document.write( "\r\n" );
document.write( "Now group the factors under the radicals into pairs\r\n" );
document.write( "of like factors as much as possible. (Note: if these\r\n" );
document.write( "had been cube roots you would have grouped by threes\r\n" );
document.write( "instead of by twos, and if they had been fourth roots\r\n" );
document.write( "you would have grouped by fours, etc.)\r\n" );
document.write( "\r\n" );
document.write( "  _____________     _______     _______\r\n" );
document.write( "3Ö(2·2)·(2·2)·3 - 2Ö(3·3)·3 - 3Ö(2·2)·3\r\n" );
document.write( "\r\n" );
document.write( "Now each pair is a square and will come out in front of the radical\r\n" );
document.write( "as a SINGLE factor.\r\n" );
document.write( "\r\n" );
document.write( "Each of the (2·2)'s comes out in front of of the 1st and 3rd radicals\r\n" );
document.write( "as a SINGLE 2 factor. \r\n" );
document.write( "\r\n" );
document.write( "The (3·3) comes out of the 2nd radical as a SINGLE 3 factor.\r\n" );
document.write( "\r\n" );
document.write( "So we have\r\n" );
document.write( "      _       _       _\r\n" );
document.write( "3·2·2Ö3 - 2·3Ö3 - 3·2Ö3\r\n" );
document.write( "\r\n" );
document.write( "or\r\n" );
document.write( "   _     _     _ \r\n" );
document.write( "12Ö3 - 6Ö3 - 6Ö3\r\n" );
document.write( "            _\r\n" );
document.write( "Factor out Ö3\r\n" );
document.write( " _\r\n" );
document.write( "Ö3(12 - 6 - 6)\r\n" );
document.write( " _\r\n" );
document.write( "Ö3(0)\r\n" );
document.write( "\r\n" );
document.write( "  0 \r\n" );
document.write( "\r\n" );
document.write( "The answer is 0.\r\n" );
document.write( "\r\n" );
document.write( "Edwin McCravy\r\n" );
document.write( "AnlytcPhil@aol.com
\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );