Square Root of 2000
2026-02-28 23:12 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-2000

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 2000, we need to group it as 00 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 × 4 = 16, which is less than or equal to 20. Now the quotient is 4. After subtracting 16 from 20, the remainder is 4.

Step 3: Bring down 00, making the new dividend 400. Double the current quotient, 4, to get 8, which will be part of our new divisor.

Step 4: We need to find a digit x such that 8x × x ≤ 400. Let us consider x as 4, now 84 × 4 = 336.

Step 5: Subtract 336 from 400, and the remainder is 64. The 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 6400.

Step 7: The new divisor will be 88 (from 84) plus the next digit x. We need to find x such that 88x × x ≤ 6400. Let us consider x as 7, now 887 × 7 = 6209.

Step 8: Subtract 6209 from 6400, and the remainder is 191.

Step 9: The quotient is now 44.7.

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 √2000 is approximately 44.72.