document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=64287>Question 64287</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you help me with rationalizing the denominator on the following:<BR>\n" );
document.write( "5 on the top, fraction bar, 9 minus radical sign 3 on the bottom (the 3 is under the radical sign) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #44933 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=44933\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To simplify:  (5)/(9-sqrt(3))\r<BR>\n" );
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document.write( "First, we want to get rid of the radical in the denominator.  We do this by multiplying the factor (9-sqrt(3)) by its conjugate (9+sqrt(3)). when we do this we get:<BR>\n" );
document.write( "(5)/(81-9sqrt3+9sqrt3-3) or\r<BR>\n" );
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document.write( "(5)/(81-3) simplifying, we have:\r<BR>\n" );
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document.write( "5/78\r<BR>\n" );
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document.write( "Note:  If the original factor is (a+b), the conjugate of (a+b) is defined as the factor that, when multiplied by the original factor, yields the answer (a^2-b^2) and that factor is (a-b)--a powerful tool for simplifying radicals and complex numbers.\r<BR>\n" );
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document.write( "Hope this helps.  Have a nice holiday season---ptaylor\r<BR>\n" );
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