Find the cube root of 4913, 12167, and 32768 by estimation.

(i) 4913

The given number is 4913

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

4 913

In this case, one group, i.e., 913 has three digits whereas 4 has only one digit.

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 7.

Step 3: Take the other group, i.e., 1. Cube of 1 is 1, so we take 1 as ten’s place of the required cube root

i.e.

(ii) 12167

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

12 167

In this case, one group, i.e., 167 has three digits whereas 12 has only one digit.

Step 2: Take 167. The digit 7 is at its one’s place. We take the one’s place of the required cube root as 3.

Step 3: Take the other group, i.e., 12. Cube of 2 is 8, and cube of 3 is 27. 12 lies between 8 and 27. The smaller number among 2 and 3 is 2. The one’s place of 2 is 2 itself. Take 2 as ten’s place of the cube root of 12167

i.e.

(iii) 32768

Step 1: Form groups of three starting from the rightmost digit of 32768

32 768

In this case, one group, i.e., 768 has three digits whereas 32 has only one digit.

Step 2: Take 768. The digit 8 is at its one’s place. We take the one’s place of the required cube root as 2.

Step 3: Take the other group, i.e., 32. Cube of 3 is 27, and cube of 4 is 64. 32 lies between 27 and 64. The smaller number among 4 and 3 is 3. The one’s place of 3 is 3 itself. Take 3 as ten’s place of the cube root of 32768

i.e.