Question

Find to five places of decimals the value of :
$\sqrt[4]{42400}$

Answer 1

given can be written as

$y=(2400{)}^{\frac{1}{4}}=(2401-1{)}^{\frac{1}{4}}$

$=(7^4-1{)}^{\frac{1}{4}}$

$=7{(1-\frac{1}{2401})}^{\frac{1}{4}}$

$=7(1-.00041{)}^{\frac{1}{4}}=7(1-(.00041).\frac{1}{4}-\frac{3}{16}.\frac{.00000016}{2!}.........)$

values are so small from third term onwards

so we can neglect them

$=7(1-(.00041).\frac{1}{4})=6.99928$