approximation?

Question

find the sqrt of 6000 by using approximation formula derived from calculus.

Answer 1

f (x) ≈ f (a) + f' (a) (x - a)

√6000
consider f(x) = x ^ 1/2
f' (x) = 1/2 x^ -1/2

f (6000) = f (6400) + f' (6400) (6000 - 6400)
= 80 - 2 .4= 77.6