- (a) Find the binomial expansion of
$$\sqrt { } ( 1 - 8 x ) , \quad | x | < \frac { 1 } { 8 }$$
in ascending powers of \(x\) up to and including the term in \(x ^ { 3 }\), simplifying each term.
(b) Show that, when \(x = \frac { 1 } { 100 }\), the exact value of \(\sqrt { } ( 1 - 8 x )\) is \(\frac { \sqrt { } 23 } { 5 }\).
(c) Substitute \(x = \frac { 1 } { 100 }\) into the binomial expansion in part (a) and hence obtain an approximation to \(\sqrt { } 23\). Give your answer to 5 decimal places.