- Given that \(k\) is a constant and the binomial expansion of
$$\sqrt { 1 + k x } \quad | k x | < 1$$
in ascending powers of \(x\) up to the term in \(x ^ { 3 }\) is
$$1 + \frac { 1 } { 8 } x + A x ^ { 2 } + B x ^ { 3 }$$
- find the value of \(k\),
- find the value of the constant \(A\) and the constant \(B\).
- Use the expansion to find an approximate value to \(\sqrt { 1.15 }\)
Show your working and give your answer to 6 decimal places.