document.write( "Question 1133242: What is the smallest positive integer which is 2 times the square of some
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Algebra.Com's Answer #750489 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "If the number is n, then\r\n" );
document.write( "\"n=2a%5E2+=+5b%5E5\"\r\n" );
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document.write( "\"2a%5E2=5b%5E5%0D%0A%0D%0A%7B%7B%7Ba%5E2+=+expr%285%2F2%29b%5E5\"\r\n" );
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document.write( "Rationalize the denominator on the right:\r\n" );
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document.write( "\"a=sqrt%2810b%5E5%29%2F2%5E%22%22\"\r\n" );
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document.write( "\"2a=sqrt%2810b%5E5%29\"\r\n" );
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document.write( "The left side is a positive integer, so the right side \r\n" );
document.write( "is also.  The smallest value of b that will cause the \r\n" );
document.write( "right side to be a positive integer is 10. \r\n" );
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document.write( "\"2a=sqrt%2810%2A10%5E5%29\"\r\n" );
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document.write( "\"2a=sqrt%2810%5E6%29\"\r\n" );
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document.write( "\"2a=10%5E3%29\"\r\n" );
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document.write( "\"2a=1000\"\r\n" );
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document.write( "\"a=500\"\r\n" );
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document.write( "So,\r\n" );
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document.write( "\"n=2a%5E2+=+2%2A500%5E2=2%2A250000+=+500000\"\r\n" );
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document.write( "So 500000 is the smallest positive integer which is 2 times \r\n" );
document.write( "the square of 500 and also 5 times 105?\r\n" );
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document.write( "Edwin
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