Making use of the cube root table,

We have:

$7300<7342<7400 \Rightarrow \sqrt[3]{7000}<\sqrt[3]{7342}<\sqrt[3]{7400}$

From the cube root table, we have: 

$\sqrt[3]{7300}=19.39$ and $\sqrt[3]{7400}=19.48$

For the difference $(7400-7300)$, i.e., 100 , the difference in values

$=19.48-19.39=0.09$

$\therefore$ For the difference of $(7342-7300)$, i.e., 42 , the difference in the values

$=\frac{0.09}{100} \times 42=0.0378=0.037$

$\therefore \sqrt[3]{7342}=19.39+0.037=19.427$