**Long Division Method to Find Square Root of 4.2025**

To find the square root of 4.2025 by long division method, follow the steps below:

**Step 1: Group the digits**
- Start by grouping the digits in pairs from right to left, including the decimal point.
- In this case, 4.2025 can be grouped as 04 and 20.25.

**Step 2: Find the largest digit**
- Determine the largest digit 'x' such that when multiplied with itself, the result is less than or equal to 04.
- In this case, the largest digit is 2, as 2 * 2 = 4, which is less than or equal to 04.

**Step 3: Write the divisor and quotient**
- Write the divisor and quotient based on the largest digit found in the previous step.
- Divisor: 2
- Quotient: 2 (as 2 * 2 = 4)

**Step 4: Find the remainder**
- Multiply the divisor and quotient obtained in the previous step.
- Subtract the result from the grouped digits.
- In this case, 2 * 2 = 4, subtracting it from 04 leaves a remainder of 0.

**Step 5: Bring down the next pair of digits**
- Bring down the next pair of digits (20) after the remainder and write it next to the remainder.
- The new number becomes 020.

**Step 6: Find the new dividend**
- Multiply the quotient obtained in the previous step by 2 and write it as the new dividend.
- Add a digit (x) at the end of the new dividend, which is unknown for now.
- The new dividend becomes 40x.

**Step 7: Find the largest digit**
- Determine the largest digit 'y' such that when the divisor is multiplied by (20y + y^2), the result is less than or equal to 40x.
- Start with y = 0 and increment it until the condition is met.
- In this case, the largest digit is 4, as 2 * (204 + 4^2) = 40x, where x = 2.

**Step 8: Write the divisor and quotient**
- Write the divisor and quotient based on the largest digit found in the previous step.
- Divisor: 2(20 + 4)
- Quotient: 24 (as 2 * (20 + 4) = 40)

**Step 9: Find the remainder**
- Multiply the divisor and quotient obtained in the previous step.
- Subtract the result from the new dividend.
- In this case, 2(20 + 4) * 24 = 40x, subtracting it from 40x leaves a remainder of 0.

**Step 10: The square root is found**
- If there are no more digits to bring down and the remainder is zero, the process ends.
- The square root of 4.2025 is 2.05.

Therefore, the square root of 4.2025 by long division method is 2.05.