document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1112825>Question 1112825</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi,<BR>\n" );
document.write( "Please help me to solve step-by-step on these questions. <BR>\n" );
document.write( "Thank you very much.<BR>\n" );
document.write( "14.<BR>\n" );
document.write( "a)<BR>\n" );
document.write( "What is the conjugate of the expression :<BR>\n" );
document.write( "	&#8730;3 + &#8730;5<BR>\n" );
document.write( "b) <BR>\n" );
document.write( "Multiply :<BR>\n" );
document.write( "	&#8730;3 + &#8730;5<BR>\n" );
document.write( "by its conjugate from part a.\r<BR>\n" );
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document.write( "	Rationalize the denominator as shown in Section 8.5 for the following rational expression :<BR>\n" );
document.write( "	(2&#8730;(5-1))/(&#8730;(3 )+&#8730;5)\r<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 #727839 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=727839\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "The conjugate of any binomial expression is created by changing the sign between the two terms, that is the conjugate of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\ +\ b\"> is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\ -\ b\">\r<BR>\n" );
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document.write( "The product of any pair of conjugates is the square of the first term minus the square of the second term.  E.g. <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( "To rationalize a binomial denominator, multiply the entire fraction by 1 in the form of the conjugate of the denominator divided by itself.\r<BR>\n" );
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document.write( "Thus:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  \(\frac{c\ +\ d}{a\ +\ b}\)\(\frac{a\ -\ b}{a\ -\ b}\)\ =\ \frac{(c\ +\ d)(a\ -\ b)}{a^2\ -\ b^2}\">\r<BR>\n" );
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document.write( "And then combine any like terms.\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" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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