How can I prove that $n \sqrt{\frac{x}{n^2}} = \sqrt{x} | n \in \mathbb{N}$?

Question

I came across this observation in an exam today, and thought that this might be useful in making certain algorithms run faster, but first I want a way to prove that this is true. How can I do this? I'm fairly new to proofs, outside of geometry and trig identities.