document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=193955>Question 193955</A>: <I><SPAN STYLE=\"word-break: break-all;\"> SIMPLIFY\r<BR>\n" );
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document.write( "THE SQUARE ROOT OF 10 -2/THE SQUARE ROOT OF 10 + 3 = </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #145724 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=145724\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "In the first place, why are you shouting at us?  All CAPS is the electronic communications equivalent of shouting, and is both rude and annoying.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\sqrt{10}-2}{\sqrt{10}+3}\">\r<BR>\n" );
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document.write( "Simplest form requires taking the radical out of the denominator.  Simply squaring the denominator won't do because you would still have a radical term because:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (a + b)^2 = a^2 + ab + b^2\">\r<BR>\n" );
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document.write( "However, multiplying the denominator by its conjugate, namely <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sqrt{10} - 3\">, works because that results in the difference of two squares, thus:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (a + b)(a - b) = a^2 - b^2\">\r<BR>\n" );
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document.write( "But you can't just multiply the denominator by something without changing the value of the rational expression.  You need to multiply by 1 in the form of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{\sqrt{10}-3}{\sqrt{10}-3}\">, thus:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(\frac{\sqrt{10}-2}{\sqrt{10}+3}\right)\left(\frac{\sqrt{10}-3}{\sqrt{10}-3}\right)\">\r<BR>\n" );
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document.write( "Apply FOIL to the numerator, and the difference of two squares result to the denominator:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{10 - 5\sqrt{10} + 6}{10 - 9} = \frac{16 - 5\sqrt{10}}{1} = 16 - 5\sqrt{10}\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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