document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=138234>Question 138234</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0078659752/algebrahomeworkh>Glencoe Mathmatics (Algebra 1)</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> 2 square root of 5<BR>\n" );
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document.write( "-4 + square root of 8 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #100935 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=100935\">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=%282sqrt%285%29%29%2F%28-4%2Bsqrt%288%29%29 ALIGN=MIDDLE  ALT=\"%282sqrt%285%29%29%2F%28-4%2Bsqrt%288%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplifying this expression involves a process called rationalizing the denominator.  The process results in a rational number in the denominator and whatever happens to the numerator as a result, happens.\r<BR>\n" );
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document.write( "You can't simply square the denominator because you would still end up with a term containing a radical, so you need another technique.  It involves using the 'difference of two squares' factorization in reverse.  Specifically, if you multiply the denominator by its conjugate (the conjugate of <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;\" > 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;\" >)\r<BR>\n" );
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document.write( "The conjugate of your denominator is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4-sqrt%288%29 ALIGN=MIDDLE  ALT=\"-4-sqrt%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now we use the multiplicative identity rule, namely <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2A1=a ALIGN=MIDDLE  ALT=\"a%2A1=a\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  But we need to multiply your fraction by 1 in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4-sqrt%288%29%29%2F%28-4-sqrt%288%29%29 ALIGN=MIDDLE  ALT=\"%28-4-sqrt%288%29%29%2F%28-4-sqrt%288%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Here's the whole thing:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282sqrt%285%29%29%2F%28-4%2Bsqrt%288%29%29%29%28%28-4-sqrt%288%29%29%2F%28-4-sqrt%288%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now all you need to do is multiply the two fractions in the normal way and simplify the result.  Let me know if you are still having difficulty with that part.<BR>\n" );
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