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Question Number 54909 by Hassen_Timol last updated on 14/Feb/19

$$Doyouknowageometricalproof$$$$oftheirrationalityofnumber\sqrt{2}?$$

Commented by kaivan.ahmadi last updated on 14/Feb/19

https://jeremykun.com/2011/08/14/the-square-root-of-2-is-irrational-geometric-proof/

Commented by kaivan.ahmadi last updated on 14/Feb/19

$$\mathrm{you}\mathrm{can}\mathrm{see}\mathrm{in}\mathrm{above}\mathrm{page}$$

Commented by Hassen_Timol last updated on 14/Feb/19

$$Thankyousir!$$

Commented by maxmathsup by imad last updated on 14/Feb/19

$$if\sqrt{2}isrationalweget\sqrt{2}=\frac{p}{q}withpandqfrom{Q}^{+★}wecantake$$$$\mathrm{\Delta }(p,q)=1\Rightarrow 2q^2=p^2\Rightarrow p^{2}iseven\Rightarrow peven\Rightarrow \mathrm{\exists }m\in N/p=2m\Rightarrow$$$$2q^2=4m^2\Rightarrow q^2=2m^2\Rightarrow q^{2}iseven\Rightarrow qiseven\Rightarrow \mathrm{\exists }{m}^{{}^{\prime }}/q=2m^{{}^{\prime }}\Rightarrow$$$$2dividepanddivideqbutthisisimpossiblebecause\mathrm{\Delta }(p,q)=1.$$

Commented by maxmathsup by imad last updated on 14/Feb/19

$$thisproofisalgebric.$$

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