document.write( "Question 652639: How do I spproximate the square root of 399 using differentials? \n" ); document.write( "
Algebra.Com's Answer #408082 by Edwin McCravy(20081)\"\" \"About 
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document.write( "We see that 399 is 1 less than 400, whose square root is 20 \r\n" );
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document.write( "We start with the square root function:\r\n" );
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document.write( " y = Ö39\r\n" );
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document.write( " y = \"+matrix%282%2C1%2C%22%22%2Cx%5E%281%2F2%29%29\"\r\n" );
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document.write( "dy = \"1%2F2\"\"+matrix%282%2C1%2C%22%22%2Cx%5E%28-1%2F2%29%29\"dx\r\n" );
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document.write( "dy = \"1%2F2\"\"+matrix%282%2C1%2C%22%22%2Cx%5E%28-1%2F2%29%29\"dx\r\n" );
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document.write( "dy = \"1%2F2\"\"+matrix%282%2C1%2C%22%22%2C1%2Fx%5E%281%2F2%29%29\"dx\r\n" );
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document.write( "dy = \"1%2F2\"\"1%2Fsqrt%28x%29\"dx\r\n" );
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document.write( "dy = \"1%2F%282sqrt%28x%29%29\"dx\r\n" );
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document.write( "We let x = 400.  The change in x = 400 to 399 is -1, so we let dx = -1\r\n" );
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document.write( "dy = \"1%2F%282sqrt%28400%29%29\"(-1) = \"-1%2F%282%2A20%29\" = \"-1%2F40\"\r\n" );
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document.write( "dy = -.025\r\n" );
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document.write( "So we add -.025 to 20\r\n" );
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document.write( "20 - .025 = 19.975\r\n" );
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document.write( "That's the approximate square root of 399.\r\n" );
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document.write( "Checking with a calculator, Ö399 = 19.97498436, very close.  \r\n" );
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document.write( "Edwin
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