Question

Find the cube root of a given number through estimation: $5832$.

Answer 1

Step $I$: Form groups of $3$ starting from right most digit of $5832$, i.e. $\overline{5}\overline{832}$.

Then, the two groups are $5$ and $832.$

Here, $5$ has $1$ digit and $832$ has $3$ digit.

Step $II$: Take $832$.

Digit in unit place $=2$.

Therefore, we take one's place of required cube root as $8$ ....[Since, $8^3=512$].

Step $III$: Now, take the other group $5$.

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.

$\therefore \sqrt[3]{35832}=18$.