2 /√7 = 2 /√7 × √7/ √7 = 2/ 7 √7
Let 2/ 7 √7 is a rational number.
∴ 2/7 √7 = p/q , where p and q are some integers and HCF(p,q) = 1 ….(1)
⇒2√7q = 7p
From (2) and (3), 7 is a common factor of both p and q, which contradicts (1).
Hence, our assumption is wrong.
Thus, 2 √7 is irrational.
