Square Root of 1233
2026-02-28 23:27 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1233

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 1233, we need to group it as 33 and 12.

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

Step 3: Now let us bring down 33, 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 will be 6n. We need to find the value of n such that 6n x n ≤ 333. Let us consider n as 5, now 65 x 5 = 325.

Step 5: Subtract 325 from 333, the difference is 8, 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 zeros to the dividend. Now the new dividend is 800.

Step 7: Now we need to find the new divisor that is 701 because 701 x 1 = 701.

Step 8: Subtracting 701 from 800, we get the result 99.

Step 9: Now the quotient is 35.1.

Step 10: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value, continue until the remainder is zero.

So the square root of √1233 is approximately 35.11.