Question

You are told that $1,331$ is a perfect cube. Can you guess without factorisation what is its cube root?

Answer 1

The given number is $1331$.
Step $I$: Form groups of three starting from the rightmost digit of $1331$. In this case one group i.e., $331$, has three digits whereas other group has only one digit i.e, $1$.
Step $II$: Take $331$, the digit $1$ is at its one's place. We know that $1$ comes at the unit's place of a number only when its cube root ends in $1$. So, we take the one's place of the required cube root as $1$.
Step $III$: Take the other group, i.e., $1$. $1^3=1$, and $2^3=8$, so, $1$ lies between $1$ and $8$. The smaller number among $1$ and $2$ is $1$. The one's place of $1$ is $1$ itself. Take $1$ as ten's place of the cube root of $1331$.
Hence, $\sqrt[3]{31331}=11$.