Obtain the binomial expansion of \(( 1 + x ) ^ { \frac { 1 } { 2 } }\) up to and including the term in \(x ^ { 2 }\).
Hence obtain the binomial expansion of \(\sqrt { 1 + \frac { 3 } { 2 } x }\) up to and including the term in \(x ^ { 2 }\).
Hence show that \(\sqrt { \frac { 2 + 3 x } { 8 } } \approx a + b x + c x ^ { 2 }\) for small values of \(x\), where \(a , b\) and \(c\) are constants to be found.