document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=333527>Question 333527</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i have understood the proof \" square root of 2 is irrational\" by contradiction method\" but i have a quesiton in my mind:\r<BR>\n" );
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document.write( "In that proof, we supposed sqrt(2) was rational with p/q in its simplest form and when it was proved that our supposition is wrong, it was automatically proved that square root 2 is irrational.... i tried the same with square root of 4 and supposed that it WAS a rational with p/q in its simplest form.. this is what happened:\r<BR>\n" );
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document.write( "p/q = sqrt(4)<BR>\n" );
document.write( "p² / q² = 4 --> equation 1<BR>\n" );
document.write( "p² = 4q²\r<BR>\n" );
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document.write( "Now:<BR>\n" );
document.write( "p² / q² = 4q² / q² (since p² = 4q²)<BR>\n" );
document.write( "or, p / q = 4q / q\r<BR>\n" );
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document.write( "but here, p/q is not in tis simplest form, so our supposition is wrong and square root of 4 is irrationa;... lol ... whats wrong with my solution??????? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #238998 by </B><A HREF=/tutors/aboutme.mpl?userid=Jk22><B>Jk22(389)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Jk22><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=Jk22><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=238998\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Now:<BR>\n" );
document.write( "p² / q² = 4q² / q² (since p² = 4q²)<BR>\n" );
document.write( "or, p / q = 4q / q \r<BR>\n" );
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document.write( "the last line should be p/q=2 (sqrt(p^2/q^2)=p/q=sqrt(4q^2/q^2)=2q/q=2) this we knew from the beginning\r<BR>\n" );
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document.write( "maybe like p^2/q^2=4 => p^2=4q^2 : p^2 is even, hence p is even, so we can write p in the form p=2m.\r<BR>\n" );
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document.write( "so : 4m^2=4q^2, but this leads no information about q (q can be odd)\r<BR>\n" );
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document.write( "------<BR>\n" );
document.write( "reminder : <BR>\n" );
document.write( "(in the case of sqrt(2), we get p^2=2q^2, the same reasoning : p^2 even, so p even, so p=2n, hence 2q^2=4n^2, so in this case we can deduce q is even too, which contradicts the simplification rule) </SPAN>\n" );
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