

Why, exactly, is the square root of 2 not a rational? - RiderOfGiraffes
http://republicofmath.wordpress.com/2010/12/03/why-exactly-is-the-square-root-of-2-not-a-rational-number/

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dnautics
Keep in mind that the square root of 2 is rational in some fields, for example
(mod 7) where sqrt(2) = 3.

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RiderOfGiraffes
And sqrt(2)=4.

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dnautics
I think this is a general result. If a number is not an integral square root,
and has a square root in F_p (and possibly Z/Zn in general) then it must have
at least one other square root.

