Prove under root 2 is a irrational no.

1.	Prove under root 2 is a irrational no.
Answer» Let √2 be a rational no. in the form a/b, where a and b are integers with no common factors other than 1.:. √2 = a/b=> a = √2b=> a²= 2b² -----(I)So, 2 is a factor of 2b² and a². Hence, 2 is also a factor of a.----(ii)Again, let 2m=a (where a is an integer)Putting a=2m in (I),(2m)²=2b²=> 4m²=2b²=> b²=2m²So,2 is a factor of 2m² and b². Hence, 2 is also a factor of b.---(iii)From (ii) and (iii),2 is the common factor of both a and b. But this is not possible, since a and b has no other factors than 1. :. Our assumption is wrong. √2 is an irrational number.

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