Find the cube-roots of 0.000027

$\sqrt[3]{0.000027}\\[1em] = \sqrt[3]{\dfrac{27}{1000000}}\\[1em] = \dfrac{\sqrt[3]{27}}{\sqrt[3]{1000000}}$

Prime factors of 27:

$\therefore \dfrac{\sqrt[3]{27}}{\sqrt[3]{1000000}} = \dfrac{\sqrt[3]{(3 \times 3\times 3)}}{\sqrt[3]{100 \times 100\times 100}}\\[1em] = \dfrac{3}{100}\\[1em] = 0.03$

Hence, $\sqrt[3]{0.000027} = 0.03$