document.write( "Question 541279: Please help me solve and explain so I can help my son understand.\r
\n" ); document.write( "\n" ); document.write( "3 - 2 radical 11 / 2 + radical 11\r
\n" ); document.write( "\n" ); document.write( "Write the equation in simplified radical form. \n" ); document.write( "
Algebra.Com's Answer #354134 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "\"%282sqrt%2811%29%29+%2F%282+%2B+sqrt%2811%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Form the conjugate of the denominator by the rule:\r\n" );
document.write( "\r\n" );
document.write( "the conjugate of A + B is A - B.  You just change the sign\r\n" );
document.write( "of the second term but keep the sign of the first term.\r\n" );
document.write( "\r\n" );
document.write( "So the conjugate of the denominator \"2+%2B+sqrt%2811%29\" is\r\n" );
document.write( "\"2+-+sqrt%2811%29\".\r\n" );
document.write( "\r\n" );
document.write( "Put this conjugate over itself like this: \"red%28%282-sqrt%2811%29%29%2F%282-sqrt%2811%29%29%29\".\r\n" );
document.write( "\r\n" );
document.write( "Since that red fraction just equals 1 we can multiply our express\r\n" );
document.write( "by it and not change its numerical value, but change its form. So we multiply\r\n" );
document.write( "by it:\r\n" );
document.write( "\r\n" );
document.write( "\"%282sqrt%2811%29%29+%2F%282+%2B+sqrt%2811%29%29\"×\"red%28%282-sqrt%2811%29%29%2F%282-sqrt%2811%29%29%29\".\r\n" );
document.write( "\r\n" );
document.write( "We'll put parentheses around the binomials:\r\n" );
document.write( "\r\n" );
document.write( "\"%282sqrt%2811%29%29+%2F%28%282+%2B+sqrt%2811%29%29%29\"×\"red%28%28%282-sqrt%2811%29%29%29%2F%28%282-sqrt%2811%29%29%29%29\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "And multiply numerators and denominators:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\"%284sqrt%2811%29-2%28sqrt%2811%29%29%5E2%29%2F%284-%28sqrt%2811%29%29%5E2%29+++++%29+++\"\r\n" );
document.write( "\r\n" );
document.write( "\"%284sqrt%2811%29-2%2A11%29%2F%284-11%29%29+++++%29+++\"\r\n" );
document.write( "\r\n" );
document.write( "\"%282%282sqrt%2811%29-11%29%29%2F%28-7%29%29+++++%29+++\"\r\n" );
document.write( "\r\n" );
document.write( "To get the negative sign off the bottom, bring it to the top:\r\n" );
document.write( "\r\n" );
document.write( "\"%28-2%282sqrt%2811%29-11%29%29%2F7%29+++++%29+++\"\r\n" );
document.write( " \r\n" );
document.write( "We can multiply the negative sign into the parentheses so it won't\r\n" );
document.write( "be sticking out in front:\r\n" );
document.write( "\r\n" );
document.write( "\"%282%28-2sqrt%2811%29%2B11%29%29%2F7%29+++++%29+++\"\r\n" );
document.write( "\r\n" );
document.write( "Finally we will reverse the terms in the parentheses:\r\n" );
document.write( "\r\n" );
document.write( "\"%282%2811-2sqrt%2811%29%29%29%2F7%29+++++%29+++\"\r\n" );
document.write( "\r\n" );
document.write( "That's the simplest form.  Or this way\r\n" );
document.write( "\r\n" );
document.write( "\"2%2F7\"\"%2811-2sqrt%2811%29%29+++++%29+++\"\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );