Square Root of 1256
2026-02-28 08:39 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1256

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 1256, we group it as 56 and 12.

Step 2: Now we need to find n whose square is ≤ 12. We can say n is ‘3’ because 3 x 3 is 9, which is less than 12. Now the quotient is 3, and after subtracting, 12 - 9, the remainder is 3.

Step 3: Now let us bring down 56 which is the new dividend. Add the old divisor with the same number 3 + 3 to get 6, which will be our new divisor.

Step 4: The new divisor is now 6n. We need to find the value of n such that 6n x n ≤ 356. Let us consider n as 5, now 6 x 5 x 5 = 150.

Step 5: Subtract 150 from 356, the difference is 206, and the quotient becomes 35.

Step 6: 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 20600.

Step 7: Now we need to find a new digit for the divisor, which is 354, because 3544 x 4 = 14176.

Step 8: Subtract 14176 from 20600, we get 6424. Step 9: Continue doing these steps until we get two numbers after the decimal point.

The square root of √1256 is approximately 35.43.