How do you use linear approximation to the square root function to estimate square roots #sqrt 4.400#?
Using binomial expansion,
Here, choose a = 66 and b = 44.
Note that the error is of order 66(1/198)^2=O(.002), nearly.
The linear approximation is a form of (or a way of thinking about) the equation of a tangent line.
Note that the equation of the line tangent to the graph at
We are not told what to use for
In this case, we want a number close to
The 'obvious' (once you see it) choice is
And we finish with
If there is a typo in the question
If the question should ask us to approximate
A bit more arithmetic will show that
To get a rough estimate use