Square Root of 1853
2026-02-28 13:27 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1853

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 1853, we need to group it as 53 and 18.

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

Step 3: Now let us bring down 53 which is the new dividend. Add the old divisor with the same number 4 + 4 = 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 ≤ 253. Let us consider n as 3, now 83 x 3 = 249.

Step 6: Subtract 253 from 249, the difference is 4, and the quotient is 43.

Step 7: Since the dividend is less than the divisor, we can add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 400.

Step 8: Now we need to find the new divisor that is 860 because 860 x 0 = 0 and 0 < 400.

Step 9: Subtracting 0 from 400, the result is 400.

Step 10: Now the quotient is 43.0

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

So the square root of √1853 is approximately 43.057.