Square Root of 2036
2026-02-28 23:39 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-2036

The long division method is particularly used for non-perfect square numbers. In this method, we check the closest perfect square number for the given number. Let's 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 2036, we group it as 36 and 20.

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

Step 3: Now let us bring down 36, which is the new dividend. Add the old divisor with the quotient, 4 + 4, to get 8, which will be our new divisor.

Step 4: Finding 8n × n ≤ 436, let us consider n as 5, now 8 x 5 x 5 = 400

Step 5: Subtract 400 from 436, the difference is 36, and the quotient is 45

Step 6: Since the dividend is less than the divisor, we add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 3600.

Step 7: We need to find the new divisor that is 901 because 901 x 4 = 3604

Step 8: Subtracting 3604 from 3600 gives us the result -4.

Step 9: The quotient is approximately 45.116

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

So the square root of √2036 ≈ 45.116