Long Division Method to Find the Square Root of 1901
To find the square root of 1901 using the long division method, follow these steps:
1. Group the number
- Start by grouping the number 1901 into pairs of digits from right to left. If there is an odd number of digits, the leftmost group will have only one digit.
- In this case, 1901 can be grouped as 19 and 01.
2. Find the largest number
- Find the largest number whose square is less than or equal to 19, which is 4 (since 4^2 = 16).
3. Divide and write
- Divide 19 by 4, which equals 4 with a remainder of 3.
- Bring down the next pair of digits (01) to the right of 3 to make 301.
4. Double the divisor
- Double the quotient (4) to get 8 and write it as the divisor with a blank space for the next digit.
5. Guess and check
- Guess a digit to place in the blank space (let's say x) and multiply 80x by x to get a number less than or equal to 301. In this case, x would be 7 because 807 * 7 = 2829.
6. Complete the division
- Subtract 2829 from 30100 to get 181 and bring down the next pair of digits (00) to make 18100.
- Double the current quotient (47) to get 94 and write it with a blank space for the next digit.
- Repeat the guess and check process until you have found the square root of 1901.
7. Final answer
- The square root of 1901 is approximately 43.63.
By following these steps, you can use the long division method to find the square root of 1901 accurately.

43.6