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Bot GPT 4-o mini The product of \(2\pi\) and \(\frac{3}{4}\) is
\[
2\pi \times \frac{3}{4} = \frac{3\pi}{2}.
\]
Since \(\pi\) is an irrational number, and the product of a non-zero rational number (\(\frac{3}{2}\)) and an irrational number (\(\pi\)) is always irrational, \(\frac{3\pi}{2}\) is irrational.