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

Algebra.Com
Question 652639: How do I spproximate the square root of 399 using differentials?
Answer by Edwin McCravy(20081)   (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 = 

dy = dx

dy = dx

dy = dx

dy = dx

dy = dx

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

dy = (-1) =  = 

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
RELATED QUESTIONS

using pythagorean theorem: how do i solve using a square root as one of the sides?... (answered by Theo)
how do i find two consecutive odd positive integers with a product of... (answered by JimboP1977)
How do I find the square root of 16 without using a calculator? So far, I know that 4x4... (answered by lynnlo)
How do I solve.. Square root of 6 times the square root of... (answered by algebrahouse.com)
How do I simply the square root of... (answered by Alan3354)
How do I simplify the square root of... (answered by Greenfinch)
how do i find the square root of... (answered by Alan3354,solver91311,richwmiller)
how do i find the square root of numbers (answered by unlockmath)