document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1084201>Question 1084201</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me to solve that the polynomial {x^2-3} is irreducible over the field of rational numbers </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #698281 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52803)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=698281\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Had it be reducible over the field of rational numbers, it would be a product of two linear polynomials.\r<BR>\n" );
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document.write( "Then it would have rational roots.\r<BR>\n" );
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document.write( "But its roots +/-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > are irrational numbers.  Contradiction which proves the base statement.\r<BR>\n" );
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