document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=748277>Question 748277</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I was working on my homework and this one stumped me. I know there can not be a radical in the denominator and I tried simplifying all of the roots before simplifying it further, but it is still giving me a bit of trouble and I would love to get help on it.\r<BR>\n" );
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document.write( "Could someone please show me how to simplify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28+8+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28+8+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28+27+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28+27+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >/<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28+6+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28+6+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28+5+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28+5+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ? Thank you for your help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #455416 by </B><A HREF=/tutors/aboutme.mpl?userid=timvanswearingen><B>timvanswearingen(106)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=timvanswearingen><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=timvanswearingen><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=455416\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When solving a problem like this, you need to multiply the top and bottom of the fraction by the conjugate of the denominator.\r<BR>\n" );
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document.write( "The conjugate is obtained by simply changing the sign between the two terms of the denominator.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%288%29-sqrt%2827%29%29%2F%28sqrt%286%29-sqrt%285%29%29 ALIGN=MIDDLE  ALT=\"%28sqrt%288%29-sqrt%2827%29%29%2F%28sqrt%286%29-sqrt%285%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=%28sqrt%288%29-sqrt%2827%29%29%2F%28sqrt%286%29-sqrt%285%29%29%2A%28sqrt%286%29%2Bsqrt%285%29%29%2F%28sqrt%286%29%2Bsqrt%285%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now the bottom will be rationalized:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%2848%29%2Bsqrt%2840%29-sqrt%28162%29-sqrt%28135%29%29%2F%286-5%29 ALIGN=MIDDLE  ALT=\"%28sqrt%2848%29%2Bsqrt%2840%29-sqrt%28162%29-sqrt%28135%29%29%2F%286-5%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=%28sqrt%2848%29%2Bsqrt%2840%29-sqrt%28162%29-sqrt%28135%29%29%2F1 ALIGN=MIDDLE  ALT=\"%28sqrt%2848%29%2Bsqrt%2840%29-sqrt%28162%29-sqrt%28135%29%29%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You can simplify the radicals a bit on top if you'd like, but it won't look much prettier.  That's it for rationalizing the denominator. </SPAN>\n" );
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