document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=238188>Question 238188</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Knowing that &#8730;2 is an irrational number, argue that &#8730;2/2 is also an irrational number.\r<BR>\n" );
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document.write( "Please help. Even just some ideas would be great. Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #175037 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=175037\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> assume that sqrt(2) / 2 is a rational number.\r<BR>\n" );
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document.write( "then you can set y = sqrt(2)/2 then this means that y is a rational number.\r<BR>\n" );
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document.write( "if you multiply both sides of this equation by 2, then you would get 2 * y = sqrt(2).\r<BR>\n" );
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document.write( "2 * y would still be a rational number because a rational number times a rational number is a rational number, but sqrt(2) would not because that's how we started.\r<BR>\n" );
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document.write( "the equation would be false negating the claim that sqrt(2) / 2 is a rational number.\r<BR>\n" );
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document.write( "how do we know that multiplying a rational number by 2 yield a rational number.\r<BR>\n" );
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document.write( "first of all 2 is a rational number because it is an integer and any integer can be represented by that number divided by 1 which is a rational number.\r<BR>\n" );
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document.write( "take the number y = 1/2\r<BR>\n" );
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document.write( "this is clearly a rational number because it's a division of two integers.\r<BR>\n" );
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document.write( "now multiply both sides of this equation by 2.\r<BR>\n" );
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document.write( "you get 2y = 1 which is also clearly a rational number because an integer is a rational number.\r<BR>\n" );
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document.write( "bottom line is the assumption that sqrt(2)/2 is a rational number is a false assumption proven by multiplying both sides of that equation by 2 yielding a false equation.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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