Prove that the product of 2pi and 3/4 is an irrational number. Find the product and explain why the value is irrational. Explain your reasoning in 1-2 sentences.

The product of \(2\pi\) and \(\frac{3}{4}\) is

\[
2\pi \cdot \frac{3}{4} = \frac{3\pi}{2}.
\]

Since \(\pi\) is an irrational number, any non-zero rational multiple of \(\pi\) (such as \(\frac{3}{2}\)) is also irrational. Therefore, \(\frac{3\pi}{2}\) is irrational, confirming that the product \(2\pi \cdot \frac{3}{4}\) is indeed irrational.