Which of the following is a perfect square as well as a cube?
343, 125, 81, or 64

Options

A. 81
B. 125
C. 343
D. 64

Answer

To determine which of the given numbers is both a perfect square and a perfect cube, we can analyze each option step by step.

### Step 1: Analyze the number 343
- **Factorization**: 343 can be expressed as \(7 \times 7 \times 7 = 7^3\).
- **Conclusion**: 343 is a perfect cube but not a perfect square.

### Step 2: Analyze the number 125
- **Factorization**: 125 can be expressed as \(5 \times 5 \times 5 = 5^3\).
- **Conclusion**: 125 is a perfect cube but not a perfect square.

### Step 3: Analyze the number 81
- **Factorization**: 81 can be expressed as \(9 \times 9 = 9^2\) or \(3 \times 3 \times 3 \times 3 = 3^4\).
- **Conclusion**: 81 is a perfect square but not a perfect cube.

### Step 4: Analyze the number 64
- **Factorization**: 64 can be expressed as \(8 \times 8 = 8^2\) or \(4 \times 4 \times 4 = 4^3\).
- **Further Breakdown**: \(8 = 2^3\), so \(8^2 = (2^3)^2 = 2^6\) and \(4^3 = (2^2)^3 = 2^6\).
- **Conclusion**: 64 is both a perfect square and a perfect cube.

### Final Conclusion
Among the numbers given, **64** is the only number that is both a perfect square and a perfect cube.

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