Question

Find to five places of decimals the value of :
${\left(1\frac{1}{250}\right)}^{\frac{1}{3}}$

Answer 1

given can be written as

$y={(1+\frac{1}{250})}^{\frac{1}{3}}=(1+.004{)}^{\frac{1}{3}}$

$=(1+.004.\frac{1}{3}-\frac{2}{9}.\frac{0.000016}{2!}.....)$

neglect terms after square term

$=(1+.0013-0.0000015)$

$=1.00299$