Prove that the product of 2π

To find the product of \( 2\pi \) and \( \frac{3}{4} \), we calculate:

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

The number \( \pi \) is known to be irrational, and the product of a non-zero rational number (\( \frac{3}{2} \)) and an irrational number (\( \pi \)) is also irrational. Therefore, \( \frac{3}{2} \pi \) is irrational.

In conclusion, \( \frac{3}{2} \pi \) is irrational because it is the product of a non-zero rational number and an irrational number.