Find the cube root of 0.064

$\sqrt[3]{0.064}\\[1em] = \sqrt[3]{\dfrac{64}{1000}}\\[1em] = \dfrac{\sqrt[3]{64}}{\sqrt[3]{1000}}$

Prime factors of 64:

$\therefore \dfrac{\sqrt[3]{64}}{\sqrt[3]{1000}} = \dfrac{\sqrt[3]{(2 \times 2 \times 2) \times (2 \times 2 \times 2)}}{\sqrt[3]{(10 \times 10 \times 10)}}\\[1em] = \dfrac{{2 \times 2}}{{10}}\\[1em] = \dfrac{{4}}{{10}}\\[1em] = 0.4$

Hence, $\sqrt[3]{0.064} = 0.4$