Question

The value of $\frac{1}{\sqrt[3]{30.027}}+{\left(\sqrt[3]{3125}\right)}^2+\sqrt{\frac{1}{\sqrt[3]{3(-21+85)}}}$ equals

• A. $25\frac{5}{6}$
• B. $26\frac{5}{8}$
• C. $28\frac{5}{6}$
• D. $28\frac{1}{6}$

Answer 1

The correct option is C $28\frac{5}{6}$

$\frac{1}{\sqrt[3]{30.027}}+(\sqrt[3]{3125}{)}^2+\sqrt{\frac{1}{\sqrt[3]{3(-21+85)}}}$

$\Rightarrow$ $\frac{1}{0.3}+(5{)}^2+\sqrt{\frac{1}{\sqrt[3]{364}}}$

$\Rightarrow$ $\frac{1}{0.3}+25+\sqrt{\frac{1}{4}}$

$\Rightarrow$ $\frac{10}{3}+25+\frac{1}{2}$

$\Rightarrow$ $\frac{20+150+3}{6}$

$\Rightarrow$ $\frac{173}{6}$

$\Rightarrow$ $28\frac{5}{6}$

$\therefore$ $\frac{1}{\sqrt[3]{30.027}}+(\sqrt[3]{3125}{)}^2+\sqrt{\frac{1}{\sqrt[3]{3(-21+85)}}}=28\frac{5}{6}$