Find the binomial expansion of \(( 1 + x ) ^ { \frac { 3 } { 2 } }\) up to and including the term in \(x ^ { 2 }\).
Find the binomial expansion of \(( 16 + 9 x ) ^ { \frac { 3 } { 2 } }\) up to and including the term in \(x ^ { 2 }\).
Use your answer to part (a)(ii) to show that \(13 ^ { \frac { 3 } { 2 } } \approx 46 + \frac { a } { b }\), stating the values of the integers \(a\) and \(b\).