Prove that the product of 2π
and 34
is an irrational number. Find the product and explain why the value is irrational. Explain your reasoning in 1–2 sentences

Answers

Answered by GPT-4o mini
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.
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