document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=110630>Question 110630</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4 over radical 5 plus radical2<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #80637 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=80637\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Not sure if your problem is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Fsqrt%285%29%2Bsqrt%282%29 ALIGN=MIDDLE  ALT=\"4%2Fsqrt%285%29%2Bsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F%28sqrt%285%29%2Bsqrt%282%29%29 ALIGN=MIDDLE  ALT=\"4%2F%28sqrt%285%29%2Bsqrt%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "I'm also not sure what you want to do with this expression, but I'll assume that you want to rationalize the denominator.<BR>\n" );
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document.write( "Let's try the second expression first.  In order to rationalize (get the radicals out of) a denominator that is the sum (or difference) of two radicals, you need to remember the factoring rule for the difference of two squares.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2-b%5E2=%28a%2Bb%29%28a-b%29 ALIGN=MIDDLE  ALT=\"a%5E2-b%5E2=%28a%2Bb%29%28a-b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%285%29%2Bsqrt%282%29%29%28sqrt%285%29-sqrt%282%29%29=%28sqrt%285%29%29%5E2-%28sqrt%282%29%29%5E2=5-2=3 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "3 is a nice neat rational denominator, so all we have to do is multiply the expression by 1, in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%285%29-sqrt%282%29%29%2F%28sqrt%285%29-sqrt%282%29%29 ALIGN=MIDDLE  ALT=\"%28sqrt%285%29-sqrt%282%29%29%2F%28sqrt%285%29-sqrt%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F%28sqrt%285%29%2Bsqrt%282%29%29%29%28%28sqrt%285%29-sqrt%282%29%29%2F%28sqrt%285%29-sqrt%282%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F3%29%28sqrt%285%29-sqrt%282%29%29 ALIGN=MIDDLE  ALT=\"%284%2F3%29%28sqrt%285%29-sqrt%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "If the problem is actually the first expression, then you need to multiply the first term by 1 in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29%2Fsqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%285%29%2Fsqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, thus:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2Fsqrt%285%29%29%28sqrt%285%29%2Fsqrt%285%29%29%2Bsqrt%282%29 ALIGN=MIDDLE  ALT=\"%284%2Fsqrt%285%29%29%28sqrt%285%29%2Fsqrt%285%29%29%2Bsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284sqrt%285%29%2F5%29%2Bsqrt%282%29 ALIGN=MIDDLE  ALT=\"%284sqrt%285%29%2F5%29%2Bsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then find a common denominator and add:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284sqrt%285%29%2B5sqrt%282%29%29%2F5 ALIGN=MIDDLE  ALT=\"%284sqrt%285%29%2B5sqrt%282%29%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope that helps.<BR>\n" );
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