document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=181310>Question 181310</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Rationalize the denominator of each expression. [] means square root.. thanks you.\r<BR>\n" );
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document.write( "[7x / [3]\r<BR>\n" );
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document.write( "3[x^2] /2[4] </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #135944 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=135944\">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( "I think you mean:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math \frac {sqrt{7x}}{sqrt{3}}\">\r<BR>\n" );
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document.write( "Rationalize the denominator means to take whatever action required so that the denominator of the fraction is a rational number.  In this case, multiplication of the denominator by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large sqrt{3}\"> will do the trick nicely.  However, you can't just multiply the denominator by something other than 1 and still have the same value for the fraction overall.  The only thing you can multiply the whole fraction by is something that has a value of 1.  In this case, it will be convenient to multiply the entire fraction by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac {sqrt{3}}{sqrt{3}}\">, thus:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math \left(\frac {sqrt{7x}}{sqrt{3}}\right)\left(\frac {sqrt{3}}{sqrt{3}}\right)= \frac {sqrt{21x}}{3}\">\r<BR>\n" );
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document.write( "Your second problem is trivial because both of the radicands are perfect squares, meaning the square roots are rational.\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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