Question 333527
Now:
p² / q² = 4q² / q² (since p² = 4q²)
or, p / q = 4q / q 

the last line should be p/q=2 (sqrt(p^2/q^2)=p/q=sqrt(4q^2/q^2)=2q/q=2) this we knew from the beginning

maybe like p^2/q^2=4 => p^2=4q^2 : p^2 is even, hence p is even, so we can write p in the form p=2m.

so : 4m^2=4q^2, but this leads no information about q (q can be odd)

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reminder : 
(in the case of sqrt(2), we get p^2=2q^2, the same reasoning : p^2 even, so p even, so p=2n, hence 2q^2=4n^2, so in this case we can deduce q is even too, which contradicts the simplification rule)