Find the value of approximated to three decimals using
the binomial theorem.
In order to use the binomial theorem, must be written in the form . Breaking out the decimal from the whole number, the expression can be written as . In this form, the binomial theorem can be used.
Remember that and , so the coefficients for the first and last term are both 1. The remaining combinations are evaluated using .
Rounded to three decimal places, is approximately 37.827.