Square Root of 2084
2026-02-28 23:36 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-2084

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 2084, we need to group it as 84 and 20.

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

Step 3: Now let us bring down 84, which is the new dividend. Add the old divisor with the same number 4 + 4, we get 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 × n ≤ 484. Let us consider n as 5, now 85 x 5 = 425.

Step 6: Subtract 425 from 484, the difference is 59, 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 5900.

Step 8: Now we need to find the new divisor, which is 457 because 457 x 7 = 3199.

Step 9: Subtracting 3199 from 5900, we get the result 2701.

Step 10: Now the quotient is 45.7.

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

So the square root of √2084 ≈ 45.64