Square Root of 1809
2026-02-28 12:47 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1809

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 1809, we need to group it as 09 and 18.

Step 2: Now we need to find n whose square is less than or equal to 18. We can say n is 4 because 4 x 4 = 16, which is less than 18. Now the quotient is 4, and after subtracting 16 from 18, the remainder is 2.

Step 3: Now let us bring down 09 which is the new dividend. Add the old divisor with the same number, 4 + 4, we get 8, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 8n as the new divisor; we need to find the value of n.

Step 5: The next step is finding 8n x n ≤ 209. Let us consider n as 2, now 82 x 2 = 164.

Step 6: Subtract 164 from 209, the difference is 45, and the quotient is 42.

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 4500.

Step 8: Now we need to find the new divisor that is 845 because 845 x 5 = 4225.

Step 9: Subtracting 4225 from 4500 we get the result 275.

Step 10: Now the quotient is 42.5.

Step 11: 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 √1809 is approximately 42.53.