Question

Find to five places of decimals the value of :
$\sqrt[3]{31003}$

Answer 1

let

$y=(1000+3{)}^{\frac{1}{3}}=10(1+.003{)}^{\frac{1}{3}}$

$=10[1+(.003)\left(\frac{1}{3}\right)-\left(\frac{.000003}{2!}\right)\left(\frac{2}{9}\right)+....]$

$=10[1+.001-.0000003]$

$=10.009997$