Making use of the cube root table,

The number $8.6$ can be written as $\frac{86}{10}$.

Now

$\sqrt[3]{8.6}=\sqrt[3]{\frac{86}{10}}=\frac{\sqrt[3]{86}}{\sqrt[3]{10}}$

By cube root table, we have:

$\sqrt[3]{86}=4.414$ and $\sqrt[3]{10}=2.154$

$\therefore \sqrt[3]{8.6}=\frac{\sqrt[3]{86}}{\sqrt[3]{10}}=\frac{4.414}{2.154}=2.049$

Thus, the required cube root is 2.049.