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

Solution

The given number is 1331

Step 1: Form groups of three starting from the rightmost digit of 1331. In this case one group 331 has three digits whereas 1 has only one digit.

Step 2: Take 331.

The digit 1 is at its one's place. We take the one's place of the required cube root as 1.

Step 3: Take the other group is 1.

Cube of 1 is 1 and cube of 2 is 8.1 lies between 0 and 8.

The smaller number between 1 and 2 is 1. The one's place of 1 is 1 itself. Take 1 as ten's place of the cube root of 1331.

Thus,

Similarly for 4913, we have

Step 1: Form groups of three starting from the rightmost digit of 4913

Step 2: Take 913

The digit 3 is at its one's place we take the one's place of the required cube root as(3 × 3 × 3 = 27) 7

Step 3: Take the other group is 4. Cube of 1 is 1 and cube of 2 is 8.4 lies between 1 and 8.

The smaller number between 1 and 2 is 1. Take 1 as ten's place of the cube root of 4913.

Thus,

Similarly for 12167, we have

Step 1: Form groups of three starting from the rightmost digit of 12167

Step 2: 7 × 7 × 7 = 343 i.e. one's place is 3

Step 3: 12, 2 × 2 × 2 = 8 and 3 × 3 × 3 = 27

8 < 12 < 27

The smaller number between 2 and 3 is 2.

The one's place of 2 is 2 it. Take 2 as tens place of the cube root of 12167.

Thus,