55 is the cuberoot of 166375 Then the value of 3√166375

SOLUTION

$\sqrt[3]{3166.375}+\sqrt[3]{30.166375}+\sqrt[3]{30.000166375}=\sqrt[3]{3\frac{166375}{1000}}+\sqrt[3]{3\frac{166375}{1000000}}+\sqrt[3]{3\frac{166375}{1000000000}}$
$=\sqrt[3]{3({\frac{55}{10})}^3}+\sqrt[3]{3({\frac{55}{100})}^3}+\sqrt[3]{3({\frac{55}{1000})}^3}$
$=\frac{55}{10}+\frac{55}{100}+\frac{55}{1000}$
$=5.5+.55+.055$
$=6.105$
Therefore, the required value is 6.105.