Prove that the product of 2π

The product of \(2\pi\) and \(34\) is given by:

\[
2\pi \times 34 = 68\pi.
\]

Since \(\pi\) is an irrational number, and the product of a non-zero rational number (68, here) and an irrational number (\(\pi\)) is also irrational, it follows that \(68\pi\) is irrational. Thus, \(2\pi \times 34 = 68\pi\) is irrational.