Square Root of 2074
2026-02-28 01:13 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-2074

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 2074, we need to group it as 20 and 74.

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

Step 3: Now let us bring down 74, 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 have 8n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 8n × n ≤ 474. Let us consider n as 5, then 85 x 5 = 425.

Step 6: Subtract 425 from 474, the difference is 49, and the quotient is 45.

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 4900.

Step 8: Now we need to find the new divisor, which is 901 because 901 x 5 = 4505.

Step 9: Subtracting 4505 from 4900, we get the result 395.

Step 10: Now the quotient is 45.5.

Step 11: Continue doing these steps until we get two numbers after the decimal point or until the remainder is zero.

So the square root of √2074 is approximately 45.54.