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Prove that the product of 2π and 3/4 is an irrational number. Find the product and explain why the value is irrational. Explain...Asked by Credance (Dark Sonic)
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
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.
\[
2\pi \times 34 = 68\pi.
\]
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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