`sqrt(9216)`

Answer

To find the square root of 9216 using the long division method, follow these steps:

### Step-by-Step Solution:

1. **Pair the Digits**: Start from the right and pair the digits of the number 9216. This gives us pairs: (92)(16).

2. **Find the Largest Square**: Look for the largest square number less than or equal to the first pair (92). The largest square is 81 (which is \(9^2\)). Write 9 above the line.

3. **Subtract and Bring Down**: Subtract 81 from 92, which gives us 11. Now, bring down the next pair (16) next to 11, making it 1116.

4. **Double the Quotient**: Double the number above the line (which is 9) to get 18. Write this down.

5. **Find the Next Digit**: Now, we need to find a digit (let's call it x) such that (180 + x) * x is less than or equal to 1116.

- Start with x = 6:
\[ (180 + 6) \times 6 = 186 \times 6 = 1116 \]
- This works perfectly.

6. **Final Calculation**: Subtract 1116 from 1116, which gives us 0. Since there are no more pairs to bring down, we conclude that the square root of 9216 is the number we found above the line, which is 96.

### Final Answer:
\[ \sqrt{9216} = 96 \]