Square Root of 1282
2026-02-28 10:48 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1282

The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square numbers 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 1282, we need to group it as 28 and 12.

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

Step 3: Now let us bring down 28, making the new dividend 328. Add the old divisor with the same number, 3 + 3, to 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, and we need to find the value of n.

Step 5: The next step is finding 6n × n ≤ 328. Let us consider n as 5, now 65 × 5 = 325.

Step 6: Subtracting 325 from 328, the difference is 3, 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 300.

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

Step 9: Subtracting 3525 from 3000, we get the result -525.

Step 10: Now the quotient is 35.7.

Step 11: Continue doing these steps until we get two numbers after the decimal point. If there are no decimal values, continue until the remainder is zero.

So the square root of √1282 is approximately 35.79.