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Question Number 159015 by Armindo last updated on 11/Nov/21

	Answered by mr W last updated on 12/Nov/21

	$s a y \sqrt{2} = \frac{p}{q} w i t h g c d (p, q) = 1$ $2 = \frac{p^{2}}{q^{2}}$ $p^{2} = 2 q^{2} \Rightarrow p = e v e n = 2 k$ $4 k^{2} = 2 q^{2}$ $q^{2} = 2 k^{2} \Rightarrow q = e v e n = 2 h$ $\Rightarrow b o t h p a n d q a r e e v e n, g c d (p, q) = 2$ $\Rightarrow c o n t r a d i c t i o n w i t h g c d (p, q) = 1$
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