Square Root of 1311
2026-02-28 01:25 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1311

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 1311, we need to group it as 11 and 13.

Step 2: Now, we need to find n whose square is less than or equal to 13. We can say n as ‘3’ because 3^2 = 9 is less than or equal to 13. Now the quotient is 3; after subtracting 9 from 13, the remainder is 4.

Step 3: Now let us bring down 11, making the new dividend 411. Add the old divisor with the same number, 3 + 3, we get 6, which will be our new divisor.

Step 4: The new divisor will be 60 (6 plus a digit to be guessed next). Now we need to find a number such that (60 + n) × n ≤ 411.

Step 5: Let us consider n as 6, so 66 × 6 = 396.

Step 6: Subtract 396 from 411; the difference is 15, and the quotient is 36.

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 zeroes to the dividend. Now the new dividend is 1500.

Step 8: Now, we need to find the new divisor, which will be 720 because 722 × 2 = 1444.

Step 9: Subtracting 1444 from 1500, we get the result 56.

Step 10: Now the quotient is 36.2.

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 √1311 is approximately 36.21.