Square Root of 1810
2026-02-28 13:50 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1810

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, group the numbers from right to left. In the case of 1810, group it as 18 and 10.

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

Step 3: Bring down 10, making the new dividend 210. 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, and we need to find the value of n.

Step 5: The next step is finding 8n x n ≤ 210. Let us consider n as 2; now 82 x 2 = 164.

Step 6: Subtract 164 from 210, the difference is 46, and the quotient is 42.

Step 7: Since the dividend is less than the divisor, add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 4600.

Step 8: Find the new divisor which is 849 because 849 x 5 = 4245.

Step 9: Subtracting 4245 from 4600 gives the result 355.

Step 10: Now the quotient is 42.5.

Step 11: Continue these steps until you have two numbers after the decimal point. If there are no decimal values, continue until the remainder is zero.

So the square root of √1810 is approximately 42.54.