$\sqrt{x} = \frac{x}{\sqrt{x}}$

Seeing the above equation may look completely logical, or not. When i saw it a few days ago, i thought it was wrong. When i understood that it was correct, i thought it was the most beautiful thing ever. I’m not 100% sure why this intrigued me so much, but it just looks great.

There are a few ways of simplifying this. We could multiply both sides with $\sqrt{x}$, like so:

$\sqrt{x} \cdot \sqrt{x} = \frac{x}{\sqrt{x}} \cdot \sqrt{x}$

$ x = \frac{x}{\sqrt{x}} \cdot \sqrt{x}$

$ x = x $

Another way would be to do cross-multiplication

$\frac{\sqrt{x}}{1} = \frac{x}{\sqrt{x}}$

$\sqrt{x} \cdot \sqrt{x} = {x} \cdot 1 $

$ x = x $

And there are probably a ton of other ways to effectively ‘solve’ this. But if there is one thing that i learned from this simple calculation, is that i actually like doing this. I’m having fun with math again!