How to prove sqrt(3) is irrational

Need to prove:

1.) If x is a real number and x^2=3, then x is irrational.

2.) The proposition "if x is a real number and x^2=4, then x is irrational." is false since x=2=2/1 is rational and 2^2=4. Pinpoint where in the previous argument the proof of this proposition breaks down.

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