Expand 1+4x4\sqrt[4]{1+4x}41+4x in ascending powers of x x\,x up to and including x3 x^3\,x3 and state the set of values of x x\,x for which the expansion is valid.
Use your expansion to find an approximation for 1.044\sqrt[4]{1.04}41.04 to 5 decimal places.