Question

You are told that 1,331 is a perfect cube. Can you guess without factorisation what is its cube root? Similarly, guess the cube roots of 32768.

Answer 1

The given perfect cube = 1331.
Forming groups of three from the rightmost digits of 1331


IInd group = 1
1st group = 331
One’s digit in first group = 1
One’s digit in the required cube root may be 1.
The second group has only 1.
Estimated cube root of 1331 = 1
Thus, $\sqrt[3]{31331}$ = 11
Now, Given perfect cube = 32768
Forming groups of three from the rightmost digits of 32768, we have


IInd group = 32
1st group = 768
One’s place digit in 768 is 8.
One’s place digit in the cube root of the given number may be 2.
Now in IInd group, we have 32
3³ < 32 < 4³
Ten’s place of the cube root of the given number = 3.
Thus, the estimated cube root of 32768 = 32.