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It's been proven that √7 and √2 are irrational.
However, I am not sure how to go about proving that √7 - √2. Is it an acceptable proof to just solve the equation which would prove/disprove the equation or as should the proof be done as a contrapositive, similar to how √7 and √2 are proven to be irrational.
What would a valid proof/disproof of irrationality look like in this case?