document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=135224>Question 135224</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Rationalize the denominator:<BR>\n" );
document.write( "8 - radical 2 divided by 6 - 3 square root 2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #99057 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=99057\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288-sqrt%282%29%29%2F%286-3sqrt%282%29%29 ALIGN=MIDDLE  ALT=\"%288-sqrt%282%29%29%2F%286-3sqrt%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The trick is to multiply the fraction by 1 in the form of the conjugate of the denominator divided by itself.\r<BR>\n" );
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document.write( "If you have an expression of the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb%2Asqrt%28c%29 ALIGN=MIDDLE  ALT=\"a%2Bb%2Asqrt%28c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then its conjugate is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-b%2Asqrt%28c%29 ALIGN=MIDDLE  ALT=\"a-b%2Asqrt%28c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and vice versa of course.\r<BR>\n" );
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document.write( "Here your denominator expression is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6-3sqrt%282%29 ALIGN=MIDDLE  ALT=\"6-3sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so the conjugate is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2B3sqrt%282%29 ALIGN=MIDDLE  ALT=\"6%2B3sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so you need to multiply your original fraction by 1 in the form of  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2B3sqrt%282%29%29%2F%286%2B3sqrt%282%29%29 ALIGN=MIDDLE  ALT=\"%286%2B3sqrt%282%29%29%2F%286%2B3sqrt%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%288-sqrt%282%29%29%2F%286-3sqrt%282%29%29%29%28%286%2B3sqrt%282%29%29%2F%286%2B3sqrt%282%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice that multiplying a binomial times its conjugate is the reverse of factoring the difference of two squares -- so the result is the first term squared minus the second term squared.  Just use FOIL on the numerator expressions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2848%2B24sqrt%282%29-6sqrt%282%29-6%29%2F%2836-18%29=%2842%2B18sqrt%282%29%29%2F18=%287%2B3sqrt%282%29%29%2F3 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The result is a fraction with a rational number in the denominator, hence the name of the process. </SPAN>\n" );
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