Question

55 is the cuberoot of 166375. Then the value of $\sqrt[3]{3166.375}+\sqrt[3]{30.166375}+\sqrt[3]{30.000166375}$ is:

• A. 6.051
• B. 6.105
• C. 6.501
• D. 6.015

Answer 1

The correct option is B 6.105

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