- (a) Use the binomial expansion, in ascending powers of \(x\), of \(\frac { 1 } { \sqrt { } ( 1 - 2 x ) }\) to show that
$$\frac { 2 + 3 x } { \sqrt { } ( 1 - 2 x ) } \approx 2 + 5 x + 6 x ^ { 2 } , \quad | x | < 0.5$$
(b) Substitute \(x = \frac { 1 } { 20 }\) into
$$\frac { 2 + 3 x } { \sqrt { } ( 1 - 2 x ) } = 2 + 5 x + 6 x ^ { 2 }$$
to obtain an approximation to \(\sqrt { 10 }\)
Give your answer as a fraction in its simplest form.