Question

Find the cube root of the given number through estimation:$2197$

Answer 1

For calculating the cube root of $2197$, this number has to be separated in two group, i.e. $2$ and $197$.

Considering the group $197$:

$197$ ends with $7$ and we know that if digit $7$ is at the end of any perfect cube number, then its cube root will have $3$ at its unit place only. Therefore, the digits at the units place of the required cube root is taken as $3$.

Now consider the other group $2$:

We know that the $1^3=1$ and $2^3=8$

Also, $1^3<2<2^3$

So, $1$ will be taken at the tens place. So, the required cube root of $2197$ is $13$.

$\sqrt[3]{32197}=13$