nth Root of 2 Is Irrational (by Fermat-Wiles)
A proof that the nth root of 2 is irrational for n ≥ 3, using Fermat's Last Theorem: hilariously overpowered, and valid.
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Cartoon by Ben Orlin, Math with Bad Drawings. https://cartoons.mathwithbaddrawings.com/2017-05-17-nth-root-of-2-is-irrational/ (CC BY-NC 4.0)Transcript
Suppose ⁿ√2 = a/b, n ≥ 3. 2 = aⁿ/bⁿ. 2bⁿ = aⁿ. bⁿ + bⁿ = aⁿ. This has no solutions, by Fermat-Wiles. Hence, [boxed] ⁿ√2 is irrational.