document.write( "Question 1043011: Prove that 7+3root2 is not a rational number. \n" ); document.write( "

Algebra.Com's Answer #658107 by ikleyn(52814) $\"\"$ $\"About$

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\n" ); document.write( "Prove that 7+3root2 is not a rational number.
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document.write( "Let assume that  is a rational number.   (1)\r\n" );
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document.write( "Then   = , where m and n are integer numbers.\r\n" );
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document.write( "Then  =  =  is the rational number.\r\n" );
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document.write( "But {{sqrt(2)}} is an irrational number  (well known fact.\r\n" );
document.write( "                                          For the proof see the lesson Proving irrationality of some real numbers in this site). \r\n" );
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document.write( "Contradiction.\r\n" );
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document.write( "You got the contradiction.\r\n" );
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document.write( "Hence, the original assumption (1) is wrong.\r\n" );
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document.write( "It implies that    is an irrational number.\r\n" );
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document.write( "The proof is completed.\r\n" );
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