Square Root by Long Division

1- 7921
To find the square root of 7921 by long division method, we follow these steps:
1. Group the digits in pairs from right to left: 79 and 21.
2. Find the largest number whose square is less than or equal to 79, which is 8.
3. Subtract the square of 8 from 79, we get 79 - 64 = 15.
4. Bring down the next pair of digits, 21.
5. Double the quotient (8) to get 16, and assume the divisor as 160.
6. Find the largest digit to add to 160 such that the new number is less than or equal to 1521 (15 and 21 combined).
7. The digit is 9, as 1609 multiplied by 9 gives 14481.
8. Subtract the square (14481) from 1521, we get 540.
9. Bring down the next pair of digits, 00.
10. Double the current quotient (1609) to get 3218, and add a placeholder for the next digit.
11. Find the largest digit to add to 32180 such that the new number is less than or equal to 54000.
12. The digit is 1, as 32181 multiplied by 1 gives 32181.
13. Subtract the square (32181) from 54000, we get 21819.
14. Bring down the next pair of digits, 00.
15. Double the current quotient (32181) to get 64362, and add a placeholder for the next digit.
16. Since the remaining number (2181900) is less than the divisor, we add another pair of zeros.
17. The square root of 7921 is 89.

2- 8649
To find the square root of 8649 by long division method, we follow the same steps as above with the given number.

3- 9801
To find the square root of 9801 by long division method, we follow the same steps as above with the given number.

4- 15129
To find the square root of 15129 by long division method, we follow the same steps as above with the given number.