document.write( "Question 683835: simplify by factoring 5 square root 96x^12y^15 \n" ); document.write( "

Algebra.Com's Answer #423788 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "Only one kind of root is called a \"SQUARE\" root.  Sometimes students\r\n" );
document.write( "get the wrong impression that all roots are called \"SQUARE\" roots, but\r\n" );
document.write( "this is false.\r\n" );
document.write( "\r\n" );
document.write( "simplify by factoring 5 square root 96x^12y^15\r\n" );
document.write( "\r\n" );
document.write( "Did you mean this ?\r\n" );
document.write( "\r\n" );
document.write( "If so that is NOT a \"SQUARE\" root but a FIFTH root.\r\n" );
document.write( "\r\n" );
document.write( "If it were as you stated it would be \r\n" );
document.write( "\r\n" );
document.write( "which is an entirely different problem.\r\n" );
document.write( "\r\n" );
document.write( "If you meant the FIFTH root, not the SQUARE root, then you change\r\n" );
document.write( " to  because 10 is the largest exponent\r\n" );
document.write( "divisible by 5.  We also change  to  or .\r\n" );
document.write( "We do not need to change  because 15 is already divisible\r\n" );
document.write( "by 5, the index of the 5th root.\r\n" );
document.write( "\r\n" );
document.write( " =  =\r\n" );
document.write( "\r\n" );
document.write( " =\r\n" );
document.write( "  \r\n" );
document.write( "Now we divide each exponent that is divisible by 5 and bring it out\r\n" );
document.write( "from under the radical with the exponent divided by the index 5:\r\n" );
document.write( "\r\n" );
document.write( " and you can drop the 1 exponent for x\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "If you really meant \"SQUARE ROOT\", like this:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then the index is understood to be 2.  I'll put the index:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "then you do not need to change  because 12 is already\r\n" );
document.write( "divisible by 2.  We change  to  or , so\r\n" );
document.write( "that the exponent 4 is divisible by 2.\r\n" );
document.write( "We change  to .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now we divide each exponent by 2 that is divisible by 2 and bring it out\r\n" );
document.write( "from under the radical with the exponent divided by the index 2:\r\n" );
document.write( "\r\n" );
document.write( " =\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "and we drop the 2 index because it's understood when the root is a\r\n" );
document.write( "SQUARE root and not some other root such as the FIFTH root.\r\n" );
document.write( "\r\n" );
document.write( " =\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );