How to find the value of $f(x)$ in the maclaurin series

Question

Using the first three non-zero terms of the Maclaurin series for

$$f(x)=(16+x)^{1/2},$$ estimate $\sqrt{15}$.

I expanded it and I got $4 + \dfrac x8 - \dfrac{x^2}{512} + \dfrac{x^3}{16384}$.

Answer 1

HINTS:

Note that $$\sqrt{15}=(16+(-1))^{1/2}$$ so substitute in $x=-1$.