SOLUTION: How do I spproximate the square root of 399 using differentials?

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Question 652639: How do I spproximate the square root of 399 using differentials?
Answer by Edwin McCravy(20081) About Me  (Show Source):
You can put this solution on YOUR website!
We see that 399 is 1 less than 400, whose square root is 20 

We start with the square root function:

 y = Ö39

 y = +matrix%282%2C1%2C%22%22%2Cx%5E%281%2F2%29%29

dy = 1%2F2+matrix%282%2C1%2C%22%22%2Cx%5E%28-1%2F2%29%29dx

dy = 1%2F2+matrix%282%2C1%2C%22%22%2Cx%5E%28-1%2F2%29%29dx

dy = 1%2F2+matrix%282%2C1%2C%22%22%2C1%2Fx%5E%281%2F2%29%29dx

dy = 1%2F21%2Fsqrt%28x%29dx

dy = 1%2F%282sqrt%28x%29%29dx

We let x = 400.  The change in x = 400 to 399 is -1, so we let dx = -1

dy = 1%2F%282sqrt%28400%29%29(-1) = -1%2F%282%2A20%29 = -1%2F40

dy = -.025

So we add -.025 to 20

20 - .025 = 19.975

That's the approximate square root of 399.

Checking with a calculator, Ö399 = 19.97498436, very close.  

Edwin