Lê Quốc Trần Anh Coordinator
06/05/2018 at 13:42
cannot be expressed in the form 
where 
and 
are rational.-
Alone 06/05/2018 at 17:07Suppose \(\sqrt{2}\) can be expressed in the form \(\dfrac{m}{n}\) with (m,n)=1
\(\Rightarrow\dfrac{m}{n}=\sqrt{2}\Rightarrow\dfrac{m^2}{n^2}=2\)\(\Rightarrow m^2=2n^2\)
Because \(2n^2⋮2\) so \(m^2⋮2\Rightarrow m⋮2\)(1)
\(\Rightarrow m^2⋮4\)\(\Rightarrow n^2⋮2\Rightarrow n⋮2\)(2)
From (1) and (2),we have the assumption is wrong
So \(\sqrt{2}\) can be expressed in the form \(\dfrac{m}{n}\)
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