- (a) Find the binomial series expansion of
$$\sqrt { 4 - 9 x } , | x | < \frac { 4 } { 9 }$$
in ascending powers of \(x\), up to and including the term in \(x ^ { 2 }\) Give each coefficient in its simplest form.
(b) Use the expansion from part (a), with a suitable value of \(x\), to find an approximate value for \(\sqrt { 310 }\)
Show all your working and give your answer to 3 decimal places.