To find the cube root of a number, we need to find a number that, when multiplied by itself three times, gives the original number. Estimation method is one way of finding the cube root of large numbers.



To use estimation method, we need to follow the steps below:

1. Divide the given number into groups of three digits from the right.
2. Find the cube root of the group of three digits on the left by using the cube root table.
3. Write the first digit of the cube root as the first digit of the answer.
4. Multiply the first digit by itself three times to get the cube of the number.
5. Subtract the cube from the group of three digits and bring down the next group of three digits.
6. Double the first digit of the answer and find the largest digit that can be multiplied by the doubled digit to get a product less than or equal to the new number.
7. Write the digit as the next digit of the answer.
8. Multiply the new digit by the previous answer, add it to the previous remainder, and repeat the process until all the groups are done.



Let's apply the estimation method to find the cube root of the following numbers:

1. 551368

- Group the digits: 551 368
- Find the cube root of 551: 8.81
- Write the first digit of the answer: 8
- Cube 8: 512
- Subtract 512 from 551: 39
- Bring down the next group of three digits: 368
- Double 8: 16
- Find the largest digit that can be multiplied by 16 to get a product less than or equal to 368: 2
- Write 2 as the next digit of the answer: 82
- Multiply 82 by 2, add it to 39, and repeat the process:
- 82 x 2 + 39 = 203
- Double 82: 164
- Find the largest digit that can be multiplied by 164 to get a product less than or equal to 203: 1
- Write 1 as the next digit of the answer: 821
- The cube root of 551368 is approximately 821.

2. 166375

- Group the digits: 166 375
- Find the cube root of 166: 5.02
- Write the first digit of the answer: 5
- Cube 5: 125
- Subtract 125 from 166: 41
- Bring down the next group of three digits: 375
- Double 5: 10
- Find the largest digit that can be multiplied by 10 to get a product less than or equal to 375: 3
- Write 3 as the next digit of the answer: 53
- Multiply 53 by 3, add it to 41, and repeat the process:
- 53 x 3 + 41 = 200
- Double 53: 106
- Find the largest digit

1. 82 ( 8 because 551 lies b/w 8³ and 9³ and 551 is closer to 8³ I.e 512 . and 2 because 8³ end with 2 and vice- versa
2. 55 ( the same reason )
3. 98
4. 63