Question

Can you guess the cube roots of the following without factorization?

$\left(\mathrm{iii}\right)32768$

Answer 1

Find the cube root using estimation

To guess the cube root of $32768$, this number has to be separated into groups of three starting from the rightmost digit.
The groups are $32$ and $768$.
When we consider the group $768$,
since $768$ ends with $8$ and we know that if the digit $8$ is at the end of any perfect cube number, then its cube root will have $2$ at its unit place only. Therefore, the digit at the unit place of the required cube root will be $2$.

When we consider the group $32$,
We know that $3^3=27$ and $4^3=64$
Also, $27<32<64$
So, $3$ will be taken at the tens place.

Hence, the cube root of $32768$ is $32$.