Question

Evaluate each of the following:

ii) $\sqrt[3]{31000}+\sqrt[3]{30.008}-\sqrt[3]{30.125}$

Answer 1

Step: Evaluate $\sqrt[3]{31000}+\sqrt[3]{30.008}-\sqrt[3]{30.125}$

$\sqrt[3]{31000}+\sqrt[3]{30.008}-\sqrt[3]{30.125}=\sqrt[3]{31000}+\sqrt[3]{3\frac{8}{1000}}-\sqrt[3]{3\frac{125}{1000}}$

$=\sqrt[3]{31000}+\frac{\sqrt[3]{38}}{\sqrt[3]{31000}}-\frac{\sqrt[3]{3125}}{\sqrt[3]{31000}}$ $[\because \sqrt[3]{3\frac{a}{b}}=\frac{\sqrt[3]{3a}}{\sqrt[3]{3b}}]$

$=\sqrt[3]{31000}+\frac{\sqrt[3]{3(2\times 2\times 2)}}{\sqrt[3]{310\times 10\times 10}}-\frac{\sqrt[3]{3(5\times 5\times 5)}}{\sqrt[3]{310\times 10\times 10}}$

$=10+\frac{2}{10}-\frac{5}{10}$

$=10+0.2-0.5$

$=9.7$

Hence, the value of $\sqrt[3]{31000}+\sqrt[3]{30.008}-\sqrt[3]{30.125}$
is $9.7$.