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Prove that the square root of 17 is irrational. Subsequently, prove that n times the square...

Prove that the square root of 17 is irrational. Subsequently, prove that n times the square root of 17 is irrational too, for any natural number n.

use the following lemma: Let p be a prime number; if p | a2 then p | a as well. Indicate in your proof the step(s) for which you invoke this lemma. Check for yourself (but you don’t have to include it in your worked solutions) that this need not be true if p is not prime.

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