Question

You are told that 1,331 is a perfect cube. Can you guess without factorization what is its cube root? Similarly guess the cube root of 4913.

Answer 1

We already know how to find the cube root of any cube number.
$\text{Step 1:}$ Take the given cube number, 1331 and start making groups of three digits starting from the right most digit of the number.
$\begin{array}{cc}\underset{–}{1}& \underset{–}{331}\\ \downarrow & \downarrow \\ \text{Second Group}& \text{First group}\end{array}$

$\text{Step 2:}$ First group i.e., 331 will give us unit's digit of the required cube root.
The number 331 ends with 1. We know that 1 comes at the unit’s place of a number only when it’s cube root ends in 1.
So, we get 1 at the unit’s place of the cube root.

$\text{Step 3:}$ Now take another group, i.e., 1.
1 is a cube number so we can take cube root of 1 as the ten’s place of the required cube root.
So, we get $\sqrt[3]{31331}=11$.

Now Moving on to the second part, We've to find the cube root of the 4913. We will repeat the same steps for this.

$\text{Step 1:}$ Take the given cube number, 4913 and start making groups of three digits starting from the right most digit of the number.
$\begin{array}{cc}\underset{–}{4}& \underset{–}{913}\\ \downarrow & \downarrow \\ \text{Second Group}& \text{First group}\end{array}$

$\text{Step 2:}$ First group i.e., 913 will give us unit's digit of the required cube root.
The number 913 ends with 3. We know that 3 comes at the unit’s place of a number only when it’s cube root ends in 7.
So, we get 7 at the unit’s place of the cube root.

$\text{Step 3:}$ Now take another group, i.e., 4.
We now that $1^3=1$ and $2^3=8$ and $1<4<8$. We take the one’s place of the smaller number as the ten’s place of the required cube root, here it is 1.
So, we get $\sqrt[3]{34913}=17$.