My sister and I are currently arguing about something regarding square roots. We'd like someone here to tell use who's right and why?

Basically, the question is: Is is true that Square root of 16 = ±4?

My reasoning is pretty simple:

Since Square root of 16 is 16^1/2, using the opposite operation, we could prove that both 4 and -4 are equal to 16^1/2 since (4)² = 16 and (-4)² = 16.

My sister's reasoning (well it's not hers since she's too stubborn to write it down...) is pretty much this:

First of all, she brought that the square root of -16 doesn't exist. I don't see the point in that, but she did... What she's basically saying is that you are finding the square root of (±4)² which then means that in can only be 4 for some magic... Honestly, I doubt she even understands her own logic...

When answering, please take into account that I want an answer that is useful for maths a 16 years old would do. Please don't include Ph.D. level reasoning!

Thank you!