Question

Find to five places of decimals the value of :
$\sqrt[5]{53128}$

Answer 1

let

$y=(3125+3{)}^{\frac{1}{5}}=5(1+.00096{)}^{\frac{1}{5}}$

$=5[1+(.00096\left)\right(\frac{1}{5})-(\frac{.0000009216}{2!}\left)\right(\frac{4}{25})+....]$

neglect third term as well

$=5[1+.000192]$

$=5.00096$