What is the square root of 7225 using the long division method?

To find the square root of 7225 using the long division method, follow these steps:

Step 1: Pair the digits
Start by pairing the digits of the number from right to left. For 7225, we divide it into pairs as follows:

72 | 25

Step 2: Find the largest number whose square is less than or equal to the first pair (72)
Look for the largest integer whose square is less than or equal to 72. The square of 8 is 64, and the square of 9 is 81, which is greater than 72. Therefore, we take 8.

Subtract the square of 8 (which is 64) from 72: 72 - 64 = 8.

Bring down the next pair (25), making the new dividend 825.

Step 3: Double the number obtained and add a suitable digit
Double the number you have obtained so far (which is 8) and write it down with a blank space to the right of it. This will be 16_.

Now, we need to find a digit to place in the blank space such that the product of (16_ and the new digit) is less than or equal to 825.

Try 5: (165 × 5 = 825).
So, the digit is 5.

Subtract 825 from 825: 825 - 825 = 0.
Step 4: Combine the digits
The digits we found are 8 and 5, so the square root of 7225 is 85.

Final Answer:
The square root of 7225 is 85.