Prove that the product of 2π

Question

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

GPT-4o mini · Answer

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.