The problem asks whether the number 342 can be classified as a perfect square, perfect cube, both, or neither. Let’s go through the definitions and check the possibilities:

1. Perfect square: A number is a perfect square if it is the square of an integer. To check if 342 is a perfect square, we can take the square root of 342 and see if the result is an integer.

   $\sqrt{342} \approx 18.49$ — Since this is not an integer, 342 is not a perfect square.

2. Perfect cube: A number is a perfect cube if it is the cube of an integer. We can check if 342 is a perfect cube by taking the cube root of 342.

   $\sqrt[3]{342} \approx 6.92$ — This is also not an integer, so 342 is not a perfect cube.

Therefore, the correct classification is that 342 is neither a perfect square nor a perfect cube.

Answer:

The correct option is D: The number is neither a perfect square nor a perfect cube because no integer squared or cubed gives 342.

Would you like more details on any of these points? Here are 5 related questions for further understanding:

1. What is a perfect square, and how can you recognize one?
2. What is a perfect cube, and how is it different from a perfect square?
3. How do you calculate square roots and cube roots manually?
4. Are there any numbers close to 342 that are perfect squares or perfect cubes?
5. Can 342 be factored into simpler components to identify any interesting properties?

Tip: When solving problems about perfect squares or cubes, using a calculator to check square and cube roots quickly can save time and help verify if the number is an integer result.