Question

Find the cube root of the number $91125$ by looking at the last digit and using estimation

Answer 1

The given number $91125$ can be written as $91,125$

Take the last group i.e. $125$

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. $91$.

To find the largest cube number we can subtract from $81$ so that the result is $\ge 0$

We can subtract $4^3=64$ from $81$, because $81-64=17\ge 0$(If we subtract $5^3=125$, we get $81-125=-44<0$).

Thus, the next neighbour digit of the answer is $4$.

Hence, $\sqrt[3]{391125}=45$