Question

Find the cube root of each of the following cube numbers through estimation.
$19683$

Answer 1

Given number $19683$.
Making the groups of the three digits starting from unit place, it can be written as $\left(19\right)\left(683\right)$
For the left most group (19), we observe that it lies between $2^3=8$ and $3^3=27$
Thus, by considering the number of remaining groups of three-digits, the required cube root lies between $20$ and $30$ as only one three digit group left.
Since, the unit digit of given number is $3$, so we can say that unit digit of cube root must be $7$ as $7^3=343$ where unit digit value is $3$.
Therefore cube root of $19683$ is $27$.
$\therefore$ $\sqrt[3]{319683}=27$