Question

Find the cube root of the number $704969$ by looking at the last digit and using estimation

Answer 1

The given number $704969$ can be written as $704,969$

Take the last group i.e. $969$

The last digit of perfect cube is $9$. So, the last digit of the cube root is $9$.

Therefore, the rightmost digit is $9$.

Now take the next group i.e. $704$.

To find the largest cube number we can subtract from $704$ so that the result is $\ge 0$

We can subtract $8^3=512$ from $704$, because $704-512=192\ge 0$

(If we subtract $9^3=729$, we get $704-729=-25<0$).

Thus, the next neighbour digit of the answer is $8$.

Hence, $\sqrt[3]{3704969}=89$