Prove that 5√2 is irrational.

assume that 5√2 is rational
⇒ 5√2 = a/b , where a and b are integers .
⇒ √2 = a/5b
we know that a, b and 5 are integers and they are also rational {i.e RHS is rational}
therefore √2 will be rational.
but we know that √2 is irrational.
there is a contradiction
so, 5√2 is an irrational number

∴ it is proved that 5√2 is irrational.