Least upper bound proof , $\{ x \in \mathbb{Q}: x^2 \le 2 \}$ [closed]

I am not super confident when it comes to proof so please bear with me. Is it possible to use proof by contradiction when trying to answer this question?

Which of the following sets of real numbers have a least upper bound? (Explain.)

a) $\{ x \in \mathbb{Q} : x^2 \le 2 \}$

My thought process is making $x$ be $5 / 1$ for example since technically it's a rational number?

That sounds super silly but I don't know. What is the best way to handle a problem like this?

If you could detailed in your explanation I would greatly appreciate it - I am really trying to learn and apply concepts.

Thanks again