Positive rationals satisfying: $a^2+a^2=c^2$? [duplicate]

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If there are none why not?

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marked as duplicate by Steven Stadnicki, Pedro Tamaroff♦, Amzoti, Start wearing purple, ClaytonJul 19 '13 at 22:39

Nigh-trivially, if there were then the square root of two would be rational ($a^2+a^2=c^2$, so $2a^2=c^2$, so $2=\frac{c^2}{a^2}$). – Steven Stadnicki Jul 19 '13 at 21:58
Note that this can be written as $$2=\left(\frac{c}a\right)^2$$
Is $\sqrt 2$ rational?