document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=488495>Question 488495</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove or disprove the product of a rational and an irrational is irrational </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #333446 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=333446\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Product of a rational and irrational is always irrational. Assume that on the contrary that a is rational, b is irrational, and their product c is rational. Then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE a*b = c\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE b = \frac{c}{a}\">\r<BR>\n" );
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document.write( "The LHS is irrational, while the RHS is a ratio of two rationals (also rational), hence contradiction. </SPAN>\n" );
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