Solution: 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.