Square Root of 12850
2026-02-21 20:43 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-12850

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 12850, we need to group it as 50 and 128.

Step 2: Now we need to find n whose square is ≤ 128. We can say n as ‘11’ because 11 x 11 = 121, which is lesser than 128. Now the quotient is 11, after subtracting 128 - 121, the remainder is 7.

Step 3: Now let us bring down 50 which is the new dividend. Add the old divisor with the same number 11 + 11 = 22, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 22n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 22n × n ≤ 750. Let us consider n as 3, now 223 x 3 = 669. Step 6: Subtract 750 from 669, the difference is 81, and the quotient is 113.

Step 7: Since the remainder is not zero, 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 8100.

Step 8: Now we need to find the new divisor that is 226 because 226 x 3 = 678.

Step 9: Subtracting 678 from 8100 we get the result 1422.

Step 10: The quotient is 113.3

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

So the square root of √12850 is approximately 113.36.