Square Root of 1286
2026-02-28 23:48 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1286

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: Group the numbers from right to left. In the case of 1286, we need to group it as 28 and 12.

Step 2: Find n whose square is less than or equal to 12. We can say n is 3 because 3^2 = 9, which is less than 12. Subtract 9 from 12, and the remainder is 3.

Step 3: Bring down 86, which makes the new dividend 386. Add the old divisor with the same number 3 + 3 to get 6 as the new divisor.

Step 4: Find 6n × n ≤ 386. Consider n as 6, now 66 x 6 = 396, which is more than 386, so try with n as 5.

Step 5: 65 x 5 = 325, which is less than 386. Subtract 325 from 386, and the remainder is 61.

Step 6: Since the dividend is less than the divisor, add a decimal point, allowing us to add two zeros to the dividend. The new dividend is 6100.

Step 7: Find the new divisor, which is 715, because 715 x 9 = 6435.

Step 8: Subtract 6435 from 6100 to get the result -335.

Step 9: Continue these steps until we get two numbers after the decimal point. If there is no remainder, continue until the remainder is zero.

So the square root of √1286 ≈ 35.85.