Final answer:
The sum of a non-zero multiple of an irrational number (√2) and a rational number (5) is always irrational, making the statement that "1/3 √2 + 5 is irrational" true.
Step-by-step explanation:
The question requires us to prove whether 1/3 √2 + 5 is rational or irrational. By definition, a rational number can be expressed as a fraction of two integers, whereas an irrational number cannot. Since √2 is known to be irrational (it cannot be expressed as a simple fraction), any non-zero multiple of it, like 1/3 √2, is also irrational. When an irrational number is added to a rational number (in this case, 5), the sum is also irrational. Therefore, the statement "1/3 √2 + 5 is irrational" is True.