document.write( "Question 291141: root of -8 / x, the problem has a little 3 in front of the root sign. I need to rationalize the denominator. \n" ); document.write( "
Algebra.Com's Answer #210621 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
root of -8 / x, the problem has a little 3 in front of the root sign. I need to rationalize the denominator. \r
\n" ); document.write( "\n" ); document.write( "
\r
\n" );
document.write( "\n" );
document.write( "\"root%283%2C-8%2Fx%29\"\r
\n" );
document.write( "\n" );
document.write( "First we can always take a negative out of a radical if the
\n" );
document.write( "index of the radical is odd. The index is 3 (That's the 
\n" );
document.write( "little 3 in front of the root sign) and therefore odd. So
\n" );
document.write( "let's take the negative sign outside:\r
\n" );
document.write( "\n" );
document.write( "\"-root%283%2C8%2Fx%29\"\r
\n" );
document.write( "\n" );
document.write( "So we need to get an exponent of 3 in the denominator.  There is
\n" );
document.write( "an \"x\" there, but we need there to be an \"x%5E3\" there, so
\n" );
document.write( "we multiply top and bottom by \"x%2Ax\"\r
\n" );
document.write( "\n" );
document.write( "\"-root%283%2C%288%2Ax%2Ax%29%2F%28x%2Ax%2Ax%29%29\"\r
\n" );
document.write( "\n" );
document.write( "\"-root%283%2C%288%2Ax%5E2%29%2F%28x%5E3%29%29\"\r
\n" );
document.write( "\n" );
document.write( "Now we use the principle \"The cube root of a quotient equals
\n" );
document.write( "the quotient of cube roots\".\r
\n" );
document.write( "\n" );
document.write( "\"-root%283%2C8%2Ax%5E2%29%2Froot%283%2Cx%5E3%29\"  \r
\n" );
document.write( "\n" );
document.write( "The denominator is now the cube root of a cube, so
\n" );
document.write( "that takes away the radical and the exponent, and just
\n" );
document.write( "leaves x in the bottom.\r
\n" );
document.write( "\n" );
document.write( "\"-root%283%2C8%2Ax%5E2%29%2Fx\"\r
\n" );
document.write( "\n" );
document.write( "Only one thing left to do, and that is to take the 
\n" );
document.write( "cube root of 8 which is 2, and put 2 on the outside
\n" );
document.write( "of the cube root:\r
\n" );
document.write( "\n" );
document.write( "\"-%282root%283%2Cx%5E2%29%29%2Fx\"\r
\n" );
document.write( "\n" );
document.write( " \n" );
document.write( "
\n" );