document.write( "Question 447435: if the product of root a and root b is irrational prove that thier sum is also irrational \n" ); document.write( "

Algebra.Com's Answer #308059 by Edwin McCravy(20056) $\"\"$ $\"About$

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document.write( "Given hypothesis:   is irrational.\r\n" );
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document.write( "To prove  is irrational\r\n" );
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document.write( "For the sake of contradiction, let's assume\r\n" );
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document.write( " is rational and equal to  where\r\n" );
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document.write( "p and q are relatively prime positive integers.\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "Solve for \r\n" );
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document.write( "The expression on the right is rational\r\n" );
document.write( "by the closure properties of addition and \r\n" );
document.write( "multiplication of rational numbers.  There is\r\n" );
document.write( "no need to simplify it unless you just want to.\r\n" );
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document.write( "So we have reached a contradiction to the\r\n" );
document.write( "given hypothesis.\r\n" );
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document.write( "Therefore the assumption that the sum of the\r\n" );
document.write( "square roots of a and b is rational is false.\r\n" );
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document.write( "Therefore the sum of the two square roots is irrational.\r\n" );
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document.write( "Edwin

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