Find the cube root of the number $166375$ by looking at the last digit and using estimation.

The given number $166375$ can be written as $166,375$

Take the last group i.e. $375$

The last digit of perfect cube is $5$. So, the last digit of the cube root is $5$.

Therefore, the rightmost digit is $5$.

Now take the next group i.e. $166$.

To find the largest cube number we can subtract from $166$ so that the result is $\ge 0$ 

We can subtract $5^3=125$ from $166$, because $166-125=41\ge 0$(If we subtract $6^3=216$, we get $166-216=-56<0$).

Thus, the next neighbour digit of the answer is $5$.

Hence, $\sqrt[3]{166375}=55$