Square Root of 2035
2026-02-28 11:39 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-2035

The long division method is particularly used for non-perfect square numbers. In this method, we need to check the closest perfect square number to 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, we need to group the numbers from right to left. In the case of 2035, we group it as 35 and 20.

Step 2: Now we need to find n whose square is closest to 20. We can say n is ‘4’ because 4 x 4 = 16, which is less than 20. The quotient is 4, and after subtracting 16 from 20, the remainder is 4.

Step 3: Bring down 35, making the new dividend 435. Add the old divisor with the same number, 4 + 4, to get 8, which will be our new divisor.

Step 4: The new divisor will be 8n. We need to find the value of n such that 8n x n ≤ 435. Let us consider n as 5, then 85 x 5 = 425.

Step 5: Subtract 425 from 435, the difference is 10, and the quotient is 45.

Step 6: Since the remainder is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the remainder. Now the new dividend is 1000.

Step 7: Now we need to find the new divisor that is 901, since 901 x 1 = 901.

Step 8: Subtracting 901 from 1000 gives the result 99.

Step 9: The quotient is 45.1

Step 10: Continue doing these steps until we get two numbers after the decimal point or until the remainder is zero.

So the square root of √2035 ≈ 45.10