Let us assume, to the contrary that 5 + 3√2 is rational.
So, we can find coprime integers a and b(b ≠ 0)
such that 5 + 3√2 = a/b
=> 3√2 = a/b - 5
=> √2 = (a - 5b)/3b
Since a and b are integers, (a - 5b)/3b is rational.
So, √2 is rational.
But this contradicts the fact that √2 is irrational.
Hence, 5 + 3√2 is irrational.