Question

Evaluate each of the following:

iv) $\sqrt[3]{3\frac{0.027}{0.008}}÷\sqrt{\frac{0.09}{0.04}}-1$

Answer 1

Step: Evaluate $\sqrt[3]{3\frac{0.027}{0.008}}÷\sqrt{\frac{0.09}{0.04}}-1$

$\sqrt[3]{3\frac{0.027}{0.008}}÷\sqrt{\frac{0.09}{0.04}}-1=\sqrt[3]{3\frac{27}{8}}÷\sqrt{\frac{9}{4}}-1$

$\sqrt[3]{3\frac{27}{8}}÷\sqrt{\frac{9}{4}}-1=\frac{\sqrt[3]{327}}{\sqrt[3]{38}}÷\frac{\sqrt{9}}{\sqrt{4}}-1$ $[\because \sqrt[3]{3\frac{a}{b}}=\frac{\sqrt[3]{3a}}{\sqrt[3]{3b}}]$

$=\frac{\sqrt[3]{327}}{\sqrt[3]{38}}\times \frac{\sqrt{4}}{\sqrt{9}}-1$

$=\frac{\sqrt[3]{33\times 3\times 3}}{\sqrt[3]{32\times 2\times 2}}\times \frac{2}{3}-1$

$=\frac{3}{2}\times \frac{2}{3}-1$

$=0$

Hence, the value of $\sqrt[3]{3\frac{0.027}{0.008}}÷\sqrt{\frac{0.09}{0.04}}-1$ is $0$.