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Prove that √3 is an irrational number.
Prove that √2 is an irrational number.
Given that √5 is an irrational number, prove that 2 + 3√5 is an irrational number.
Show that √2 − √5 is an irrational number.
Prove that 3 + 7√2 is an irrational number, given that √2 is an irrational number.
Prove that (7 − 2√3) is an irrational number, given that √3 is an irrational number.
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