Question

Find to five places of decimals the value of :
$\frac{1}{\sqrt[3]{3128}}$

Answer 1

let

$y=(125+3{)}^{\frac{-1}{3}}=\frac{1}{5}(1+.024{)}^{\frac{-1}{3}}$

$=\frac{1}{5}[1-(.024)\left(\frac{1}{3}\right)+\left(\frac{.000576}{2!}\right)\left(\frac{4}{9}\right)+....]$

$=\frac{1}{5}[1-.008+.000128]$

$=0.19842$