Evaluate: $\sqrt[3]{0.729}\p\sqrt{0.0009}\times( 0.25)^{\frac{1}{2}}-\sqrt[3]{3.75}$.

Given: $\sqrt[3]{0.729}\div\sqrt{0.0009}\times( 0.25)^{\frac{1}{2}}-\sqrt[3]{3.75}$.

To do: To evaluate: $\sqrt[3]{0.729}\div\sqrt{0.0009}\times( 0.25)^{\frac{1}{2}}-\sqrt[3]{3.75}$.

Solution:

$\sqrt[3]{0.729}\div\sqrt{0.0009}\times( 0.25)^{\frac{1}{2}}-\sqrt[3]{3.75}$

$=\sqrt[3]{\frac{729}{1000}}\div\sqrt{\frac{9}{10000}}\times( \frac{25}{100})^{\frac{1}{2}}-\sqrt[3]{\frac{375}{100}}$

$=\sqrt[3]{\frac{9\times9\times9}{10\times10\times10}}\div\sqrt{\frac{3\times3}{100\times100}}\times( \frac{5\times5}{10\times10})^{\frac{1}{2}}-\sqrt[3]{\frac{3\times5\times5\times5}{10\times10}}$

$=\frac{9}{10}\div\frac{3}{100}\times( \frac{5}{10})-\frac{19.36}{10}$

$=\frac{9}{10}\times\frac{100}{3}\times\frac{5}{10}-\frac{19.36}{10}$

$=15-1.9$

$=13.1$