Square Root of 1268
2026-02-28 17:32 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1268

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 1268, we need to group it as 68 and 12.

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

Step 3: Now let us bring down 68, which is the new dividend. 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 the sum of the dividend and quotient. Now we get 6n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 6n × n ≤ 368. Let us consider n as 6; now 6 × 6 = 36, and 66 × 6 = 396, which is greater than 368, so we try n as 5.

Step 6: Subtracting 330 (65 × 5) from 368, the difference is 38, and the quotient is 35.

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 3800.

Step 8: Now we need to find the new divisor, which is 705, because 705 × 5 = 3525.

Step 9: Subtracting 3525 from 3800, we get the result 275.

Step 10: Now the quotient is 35.5.

Step 11: Continue doing these steps until we get two numbers after the decimal point.

So the square root of √1268 ≈ 35.60.