Square Root of 1206
2026-02-28 10:09 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1206

The long division method is particularly used for non-perfect square numbers. This method involves finding 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 1206, we need to group it as 06 and 12.

Step 2: Now we need to find n whose square is ≤ 12. We can say n is 3 because 3 x 3 = 9, which is less 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 06, 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, where we need to find the value of n such that 6n x n ≤ 306.

Step 5: Let us consider n as 5, now 65 x 5 = 325, which is too large, so we try n = 4.

Step 6: Subtract 264 (64 x 4) from 306, the difference is 42, and the quotient is 34.

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 4200.

Step 8: Find the new divisor, which is 689 because 689 x 6 = 4134.

Step 9: Subtracting 4134 from 4200, we get the result 66.

Step 10: Now the quotient is approximately 34.7.

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

So the square root of √1206 is approximately 34.74.