Which of the following numbers will have an irrational square root

Options

A. 9216
B. 6561
C. 8192
D. 2704

Answer

To determine which of the given numbers has an irrational square root, we need to analyze each option based on whether they are perfect squares or not. A perfect square is a number that can be expressed as the square of an integer.

### Step-by-Step Solution:

1. **Identify the Options**:
- Option A: 9216
- Option B: 6561
- Option C: 8192
- Option D: 2704

2. **Check Each Number**:
- **Option A: 9216**
- Calculate the square root:
\(\sqrt{9216} = 96\) (since \(96 \times 96 = 9216\))
- Conclusion: 9216 is a perfect square.

- **Option B: 6561**
- Calculate the square root:
\(\sqrt{6561} = 81\) (since \(81 \times 81 = 6561\))
- Conclusion: 6561 is a perfect square.

- **Option C: 8192**
- Calculate the square root:
\(\sqrt{8192} \approx 90.51\) (not an integer)
- Conclusion: 8192 is not a perfect square, hence it has an irrational square root.

- **Option D: 2704**
- Calculate the square root:
\(\sqrt{2704} = 52\) (since \(52 \times 52 = 2704\))
- Conclusion: 2704 is a perfect square.

3. **Final Conclusion**:
- Among the options, only **8192** does not have a perfect square root. Therefore, it has an irrational square root.

### Answer:
The number that will have an irrational square root is **8192**.