document.write( "Question 485329: prove that, square root of 2 is not a rational number. \n" ); document.write( "

Algebra.Com's Answer #331953 by richard1234(7193) $\"\"$ $\"About$

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Assume that sqrt(2) is a rational number, i.e.\r
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where a and b are integers and a/b is irreducible. Squaring both sides,\r
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this implies that since the LHS is even, then the RHS is also even, and a is a multiple of 2. We can write 2k instead of a:\r
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\n" ); document.write( "\n" ); document.write( "Similarly, we can write b as 2m for some integer m. This contradicts our original statements, because this would imply a = 2k, b = 2m and they are not in simplest form (plus, we can apply this technique infinitely many times -- also not good). Hence we have a contradiction and sqrt(2) is irrational. \n" ); document.write( "

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