Question

sqrt(399), how do i solve it using linear approximation?

Answer 1

Can you think of a number close to 399 whose square root would be easy to calculate?

Answer 2

400

Answer 3

Do you know the 'formula' that you could use? We will use the fact that sqrt(400)=20

Answer 4

Does \[y - y_{0} = f'(x_{0}) \times (x - x_0)\] look familiar?

Answer 5

Our \[f(x) = x^{\frac{1}{2}}\] here, as we are trying to approximate a square root.

So we could do

\[f(399) \approx f(400) + f'(400) \times (399-400)\]

Do you see why?