document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=779713>Question 779713</A>: <I><SPAN STYLE=\"word-break: break-all;\"> prove that: 7-2 root 3 is an irrational number </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #475339 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=475339\">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( "Theorem 1:  The square root of any non-negative integer that is not a perfect square is irrational.\r<BR>\n" );
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document.write( "Theorem 2:  The product of a rational number and an irrational number is irrational.\r<BR>\n" );
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document.write( "Theorem 3:  The sum of a rational number and an irrational number is irrational.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sqrt{3}\"> is irrational by Theorem 1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 2\"> is an integer and therefore rational by definition.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 2\sqrt{3}\"> is irrational by Theorem 2.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 7\"> is an integer and therefore rational by definition.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 7\ -\ 2\sqrt{3}\"> is irrational by Theorem 3.\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( "<font face=\"Math1\" size=\"+2\">Egw to Beta kai to Sigma</font><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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