Let 5√2 is a rational number.
∴ 5√2 = p/q , where p and q are some integers and HCF(p, q) = 1 …(1)
Let p = 2m, where m is some integer.
From (2) and (3) is a common factor of both p and q, which contradicts (1).
Hence, our assumption is wrong.
Thus, 5√2 is irrational.