Problem

$$\mathrm{f}(x)=\sqrt{1-4x^2}\qquad |x|<\frac{1}{2}$$

(a) Find, in ascending powers of $x$, the first four non-zero terms of the binomial expansion of $\mathrm{f}(x)$. Give each coefficient in simplest form.

(b) By substituting $x=\dfrac{1}{4}$ into the binomial expansion of $\mathrm{f}(x)$, obtain an approximation for $\sqrt{3}$

Give your answer to 4 decimal places.