Question

Evaluate each of the following:

i) $\sqrt[3]{327}+\sqrt[3]{30.008}+\sqrt[3]{30.064}$

Answer 1

Step: Evaluate $\sqrt[3]{327}+\sqrt[3]{30.008}+\sqrt[3]{30.064}$

$\sqrt[3]{327}+\sqrt[3]{30.008}+\sqrt[3]{30.064}=\sqrt[3]{327}+\sqrt[3]{3\frac{8}{1000}}+\sqrt[3]{3\frac{64}{1000}}$

$=\sqrt[3]{327}+\frac{\sqrt[3]{38}}{\sqrt[3]{31000}}+\frac{\sqrt[3]{364}}{\sqrt[3]{31000}}$ $[\because \sqrt[3]{3\frac{a}{b}}=\frac{\sqrt[3]{3a}}{\sqrt[3]{3b}}]$

$=\sqrt[3]{327}+\frac{\sqrt[3]{3(2\times 2\times 2)}}{\sqrt[3]{310\times 10\times 10}}+\frac{\sqrt[3]{3(4\times 4\times 4)}}{\sqrt[3]{310\times 10\times 10}}$

$=3+\frac{2}{10}+\frac{4}{10}$

$=3+0.2+0.4$

$=3.6$

Hence, the value of $\sqrt[3]{327}+\sqrt[3]{30.008}+\sqrt[3]{30.064}$ is $3.6$.