Question

You are told that $1331$ is a perfect cube. Can you guess without factorisation what is its cube root? Similarly, guess the cube root of $4913,12167,32768$.

Answer 1

The given number is $1331$.

Let us form groups of three digits starting from rightmost digit.

Therefore, the two groups are $\underset{–}{1}$ and $\underset{–}{331}$.

Consider the group : $331$

We take the unit's place of required cube root as $1$

Consider the group : $1$

The unit's place of 1 is 1 itself. So, we take $1$ as ten's place of cube root of $1331$ as $1$.

Thus, $\sqrt[3]{31331}=11$.

Similarly,

$4913\Rightarrow \underset{–}{4}$ and $\underset{–}{913}$

$\therefore \sqrt[3]{34913}=17$

$12167\Rightarrow \underset{–}{12}$ and $\underset{–}{167}$

$\therefore \sqrt[3]{312167}=23$

$32768\Rightarrow \underset{–}{32}$ and $\underset{–}{768}$

$\therefore \sqrt[3]{332768}=32$