Answer :

at the very first we will create groups of three digits starting from the rightmost digit of the number as 1̅ 3̅3̅1̅

Now, There are 2 groups, having 1 and 331, in it

Taking 331,

Its digit at the unit place is 1.

We know,

If the digit 1 is at the end of a perfect cube number, then its cube root will have its unit place digit as 1 only.

Hence, the unit place digit of the required cube root can be taken as 1

Taking the next group i.e., 1, the cube of 1 exactly matches with the number of the second group. Therefore, the tens digit of our cube root will be taken as the unit place of the smaller number whose cube is close to the number of the second group i.e., 1 itself. 1 will be taken as tens place of the cube root of 1331.

Hence,

The cube root of 4913 has to be calculated.

We will make groups of three digits starting from the right side digit of 4913, as 4̅ 9̅1̅3̅. Hence, the groups are 4 and 913.

Taking the group 913, the unit digit of the number 913 is 3.

We know that if the digit 3 is at the end of a perfect cube number, then its cube root will have its unit place digit as 7 only.

Hence, the unit place digit of the required cube root is taken as 7.

Now,

Considering the other group i.e., 4,

We know that,

1^{3} = 1 and 2^{3} = 8

And,

1 < 4 < 8

Therefore, 1 will be taken at the tens place of the required cube root

Hence,

Now,

The cube root of 12167 has to be calculated.

Again we will create groups of three digits starting from the right side digit of the number 12167, as 1̅2̅ 1̅6̅7̅. The groups are 12 and 167

Analyzing the group 167,

167 ends with 7 We know that if the digit 7 is at the end of a perfect cube number, then its cube root will have its unit place digit as 3 only. Therefore, the unit place digit of the required cube root can be considered as 3.

Now,

Analyzing the other group i.e., 12,

We know that,

2^{3} = 8 and 3^{3} = 27

And,

8 < 12 < 27

2 is smaller between 2 and 3.

Therefore, 2 will be taken at the tens place of the required cube root.

Hence,

The cube root of 32768 is to be calculated.

We will create groups of three digits starting from the right side digit of the number 32768, as 3̅2̅ 7̅6̅8̅

Analyzing, the group 768,

768 ends with 8 We know that if the digit 8 is at the end of a perfect cube number, then its cube root will have its unit place digit as 2 only.

Hence, the unit place digit of the required cube root will be taken as 2

Taking the other group i.e., 32,

We know that, 3^{3} = 27 and 4^{3} = 64

And,

27 < 32 < 64

3 is smaller between 3 and 4.

Therefore, 3 will be taken at the tens place of the required cube root.

Thus,

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