Square Root of 2625
2026-02-28 00:49 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-2625

The long division method is used for non-perfect square numbers. In this method, we find 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 2625, we need to group it as 25 and 26.

Step 2: Now, we need to find a number whose square is less than or equal to 26. We can say it is '5' because 5^2 = 25, which is less than or equal to 26. The quotient is 5, and after subtracting, 26 - 25, the remainder is 1.

Step 3: Bring down the next pair of digits (25), making the new dividend 125. Add the previous divisor (5) to itself to make the new divisor 10.

Step 4: Now, we need to find a digit that, when added to 10 and multiplied by the same digit, the product is less than or equal to 125. Let's choose 1. So, 101 x 1 = 101.

Step 5: Subtract 101 from 125, the difference is 24, and the quotient is 51.

Step 6: Since the new dividend is smaller than the new divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend, making it 2400.

Step 7: Find the new divisor, which is 102. Choose a digit, say 4, such that 1024 x 4 = 4096.

Step 8: Subtract 4096 from 2400, resulting in a negative number, so we need to adjust our choice. Choose 2 instead, so 1022 x 2 = 2044.

Step 9: Now, the remainder is 356, and the quotient becomes 51.2.

Step 10: Continue these steps until we get the desired precision.

The square root of √2625 ≈ 51.23475.