prove that 2 upon under root 7 is irrational number

1.	prove that 2 upon under root 7 is irrational number
Answer» First assume 2/root7 is rationalSo,2/root 7=a/b ( a and are coprime number Square both side, we get,4/7=a²/b²4b²/7=a²So 4/7 is factor of a²So 4/7 is also factor of a (by theorem)Now let a=4/7c ( for any integer c) so we get, (4/7c)²=4b²/716/49c²=4b²/7b²=4/7c²So 4/7 is factor of b² So 4/7 is also factor of bSo a and b are not coprime So our assumption is wrong So 2/root7 is irrational number (This is proved by contradiction method)

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