Square Root of 2005
2026-02-21 20:38 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-2005

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 2005, we need to group it as 05 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 lesser than or equal to 20. Now the quotient is 4, and the remainder is 20 - 16 = 4.

Step 3: Now let us bring down 05, giving us a new dividend of 405. Add the old divisor with the same number: 4 + 4 = 8, which will be our new divisor.

Step 4: We need to find the largest possible digit x such that 8x * x ≤ 405. For x = 5, 85 * 5 = 425, which is more than 405. For x = 4, 84 * 4 = 336, which is less than 405.

Step 5: Subtract 336 from 405; the remainder is 69. Our quotient is now 44.

Step 6: 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 6900.

Step 7: Find the new divisor, 88, by adding 4 to the quotient, making it 88x. Determine x such that 88x * x ≤ 6900. For x = 7, 887 * 7 = 6209.

Step 8: Subtracting 6209 from 6900 gives us a remainder of 691.

Step 9: The quotient is now 44.7.

Step 10: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.

So the square root of √2005 is approximately 44.78.