The multiplication of \( \sqrt{*} \) (assuming \( * \) represents a non-specified positive number) and \( \frac{4}{5} \) can be analyzed based on the nature of the square root.
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If \( * \) is a perfect square, then \( \sqrt{*} \) would be a rational number (because the square root of a perfect square is an integer, which is a rational number). Multiplying a rational number by another rational number (like \( \frac{4}{5} \)) will result in a rational number.
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If \( * \) is not a perfect square, then \( \sqrt{} \) will be an irrational number. When you multiply an irrational number (like \( \sqrt{} \)) by a rational number (like \( \frac{4}{5} \)), the result will still be an irrational number.
Given we don't have specific information about whether \( * \) is a perfect square or not, we can conclude:
- If \( * \) is a perfect square, the result will be a rational number.
- If \( * \) is not a perfect square, the result will be an irrational number.
Since the problem doesn't specify \( * \), the answer can vary based on this condition. However, focusing on the choices given, generally:
- The best generic answer is an irrational number, since that encompasses the broader possibility of \( * \) not being a perfect square.
So, the final answer is an irrational number.