Question

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

Answer 1

Step $I$: Form groups of $3$ starting from right most digit of $2197$, i.e. $\overline{2}\overline{197}$.

Then, the two groups are $2$ and $197.$

Here, $2$ has $1$ digit and $197$ has $3$ digit.

Step $II$: Take $197$.

Digit in unit place $=7$.

Therefore, we take one's place of required cube root as $3$ ....[Since, $3^3=27$].

Step $III$: Now, take the other group $2$.

We know, $1^3=1$ and $2^3=8$.

Here, the smallest number among $1$ and $2$ is $1$.

Therefore, we take $1$ as ten's place.

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