document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=163585>Question 163585</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I know I have to rationalize the denominator, im just not sure how it works with a square root and real number. Help, please! Thanks, Elizabeth.\r<BR>\n" );
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document.write( "  11<BR>\n" );
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document.write( "&#8730;7 + 8\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "    3<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "2&#8730;5 - &#8730;7\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #122732 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=122732\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I know I have to rationalize the denominator, im just not sure how it works with a square root and real number. Help, please! Thanks, Elizabeth. <BR>\n" );
document.write( "11<BR>\n" );
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document.write( "&#8730;7 + 8 <BR>\n" );
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document.write( "Use the \"conjugate\" to get rid of radicals in the DEN.  Multiply NUM and DEN by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%287%29-+8 ALIGN=MIDDLE  ALT=\"sqrt%287%29-+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "[11*(sqrt(7) -8]/(7 - 64)<BR>\n" );
document.write( "= -<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2811%2Asqrt%287%29+-+8%29%2F57 ALIGN=MIDDLE  ALT=\"%2811%2Asqrt%287%29+-+8%29%2F57\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiplying by the \"conjugate\" is something you'll see more of to deal with radicals and imaginaries.\r<BR>\n" );
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document.write( "and <BR>\n" );
document.write( "3<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "2&#8730;5 - &#8730;7 <BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "Same approach, multiply by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%285%29+%2B+sqrt%287%29 ALIGN=MIDDLE  ALT=\"2sqrt%285%29+%2B+sqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A%282sqrt%285%29+%2B+sqrt%287%29%29%2F%2820+-+7%29 ALIGN=MIDDLE  ALT=\"3%2A%282sqrt%285%29+%2B+sqrt%287%29%29%2F%2820+-+7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286sqrt%285%29+%2B+3sqrt%287%29%29%2F13 ALIGN=MIDDLE  ALT=\"%286sqrt%285%29+%2B+3sqrt%287%29%29%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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