Question

You are told that 2,331 is a perfect cube . Can you guess without factorisation what is its cube root ? Similarly , guess the cube root of 4013, 12167,32768​

Answer 1

Answer:

1. 1331

Let us divide 1331 into groups of three digits starting from the right. So 1331 has two groups, one is 331 and another is 1.

For first group 331, digit 1 is at one's place. 1 comes at the unit's place of a number only when its cube root ends with 1. So unit's place of the required cube root is 1.

For another group, i.e. 1,1

3

=1 and 2

3

=8. So 1 lies between 0 and 8. The smaller number among 1 and 2 is 1. So the one's place of 1 is 1 and ten's place of cube root 1331 is 1

Hence

3

1331

=11

2. 4913

Let us divide 4913 into groups of three-digit starting from the right. So 4913 has two groups one is 913 and another is 4.

For first group 913, the digit 3 is at unit's place. 3 comes at the unit's place of a number only when its cube root ends in 7. So unit's place of the required cube root is 7.

For another group, i.e. 4, we know that 1

3

=1 and 2

3

=8. We know that 4 lies between 1 and 8. The smaller number among 1 and 2 is 1. So the one's place of 1 is 1$ and ten's place of cube root 4913 is 1

Hence

3

4913

=17

3. 12167

Let us divide 12167 into groups of three-digit starting from the right. So 12167 has two groups one is 167 and another is 12.

For first group 167, the digit 7 is at unit's place. 7 comes at a unit place of a number only when its cube root ends in 3. So unit's place of the required cube root is 3.

For another group, i.e. 12, we know that 2

3

=8 and 3

3

=27. We find that 12 lies between 8 and 27. The smaller number among 2 and 3 is 2. So the one's place of 2 is 2 itself and ten's place of cube root 12167 is 2

Hence

3

12167

=23

4. 32768

Let us divide 32768 into groups of three-digit starting from the right. So 32768 has two groups one is 768 and another is 32.

For first group 768, the digit 8 is at unit's place. 8 comes at the unit place of a number only when its cube root ends in 2. So unit's place of the required cube root is 2.

For another group, i.e. 32,3

3

=27 and 4

3

=64. So 32 lies between 27 and 64. The smaller number among 3 and 4 is 4. So the ten's place of cube root 32768 is 3

Hence

3

32768

=32