Making use of the cube root table,

We have:

$830<833<840 \Rightarrow \sqrt[3]{830}<\sqrt[3]{833}<\sqrt[3]{840}$

From the cube root table, we have: 

$\sqrt[3]{830}=9.398$ and $\sqrt[3]{840}=9.435$

For the difference $(840-830)$, i.e., 10 , the difference in values

$=9.435-9.398=0.037$

$\therefore$ For the difference $(833-830)$, i.e., 3 , the difference in values

$=\frac{0.037}{10} \times 3=0.0111=0.011$ (upto three decimal places)

$\therefore \sqrt[3]{833}=9.398+0.011=9.409$