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Cornell2017

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This is my first post to Physics Forums. If I posted this question in the wrong area or am violating some other etiquette, please let me know!

I'm working on a proof and am currently stuck. I'm trying to prove that x (a weird number, an infinite product to be specific), is NOT a perfect square. At first I thought I could say that if x converges to a value between two perfect squares, it then can't be a perfect square. Then I realized that 1, 4, 9, 16, 25,... are not the only perfect squares. There are also 0.16 (0.4^2), 6.25 (2.5^2), etc. How could I go about showing that x is a perfect square? or that sqrt(x) is irrational?

I'd really appreciate some guidance on this!

Thanks so much!

Justin