Why isn't $\sqrt{2} = \frac{\sqrt{2}}{1}$ rational?

Question

Well, I know that $\sqrt{2}$ is an irrational number and I am also familiar with the proof by contradiction method, but I'm confused by this notation as we can divide $\sqrt{2}$ by $1$ (as $\sqrt{2}$ is a real number and for a real number it is possible) and will get $\sqrt{2}$, so can't $\sqrt{2}$ be written as $\frac{\sqrt{2}}{1}$, and in that case $\sqrt{2}$ should be a rational number.