What is the square root of 2025 by long division method?

The square root of 2025, calculated using the long division method, is 45.

Long Division Method Explained

The long division method is a systematic approach to finding the square root of a number. Here's how it works for 2025, based on the reference provided:

1. Grouping: Begin by grouping the digits of the number (2025) into pairs, starting from the right. So, we have 20 and 25.

2. Finding the First Digit: Find the largest number whose square is less than or equal to the first group (20). That number is 4 (since 4² = 16). Write 4 as the first digit of the square root.

3. Subtraction and Bringing Down: Subtract 16 from 20, which leaves 4. Bring down the next group of digits (25) to form 425.

4. Finding the Next Digit: Double the first digit of the square root (4 x 2 = 8). Find a digit (let's call it 'x') such that 8x multiplied by x is less than or equal to 425. In this case, x = 5 works best (85 x 5 = 425).

5. Final Steps: Write 5 as the next digit of the square root. Divide 425 by 85, resulting in a quotient of 5 and a remainder of 0 (425 - 85 x 5 = 0).

6. Termination: The process stops when the remainder is 0 and there are no more digits to bring down. The square root is thus 45. The reference confirms, "Therefore, the square root of 2025 by the long division method is 45."