Square Root of 1223
2026-02-28 09:14 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1223

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 1223, we need to group it as 23 and 12.

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

Step 3: Now let us bring down 23, which is the new dividend. Add the old divisor with the same number, 3 + 3, and 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 ≤ 323; let us consider n as 5, now 65 x 5 = 325

Step 6: Since 325 is greater than 323, let us consider n as 4. Now 64 x 4 = 256

Step 7: Subtract 256 from 323; the difference is 67, and the quotient is 34.

Step 8: 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 6700.

Step 9: Now we need to find the new divisor that is 9 because 679 x 9 = 6111

Step 10: Subtracting 6111 from 6700, we get the result 589.

Step 11: Now the quotient is 34.9 Step 12: 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 √1223 is approximately 34.96.