Find the coefficient of \(x ^ { 5 }\) in the expansion of \(( 3 - 2 x ) ^ { 8 }\).
Expand \(( 1 + 3 x ) ^ { 0.5 }\) as far as the term in \(x ^ { 3 }\).
State the range of values of \(x\) for which your expansion is valid.
A student suggests the following check to determine whether the expansion obtained in part (b)(i) may be correct.
"Use the expansion to find an estimate for \(\sqrt { 103 }\), correct to five decimal places, and compare this with the value of \(\sqrt { 103 }\) given by your calculator."
Showing your working, carry out this check on your expansion from part (b)(i).