Square Root of 3121
2026-02-28 10:11 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-3121

The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step:

Step 1: To begin with, we need to group the numbers from right to left. In the case of 3121, we need to group it as 21 and 31.

Step 2: Now we need to find n whose square is less than or equal to 31. We can say n is 5 because 5 × 5 = 25 which is less than 31. Now the quotient is 5, and after subtracting 25 from 31, the remainder is 6.

Step 3: Bring down 21 which is the new dividend. Add the old divisor with the same number 5 + 5, we get 10 which will be our new divisor.

Step 4: The new divisor will be the sum of the previous quotient and divisor. Now we get 10n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 10n × n ≤ 621. Let us consider n as 5, now 105 × 5 = 525.

Step 6: Subtract 621 from 525, the difference is 96, and the quotient is 55.

Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeros to the dividend. Now the new dividend is 9600.

Step 8: Now we need to find the new divisor that is 558 because 558 × 8 = 4464.

Step 9: Subtracting 4464 from 9600 we get the result 5136.

Step 10: Now the quotient is 55.8.

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero. So the square root of √3121 is approximately 55.83.