The product of \( \pi \) and \( \frac{3}{4} \) will be an irrational number.
This is because \( \pi \) is known to be an irrational number, and the product of a non-zero rational number (like \( \frac{3}{4} \)) and an irrational number is also irrational. Therefore, the correct response is:
an irrational number.