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!
The definition of "square root" as a function is commonly defined to be specifically the POSITIVE number that when squared gives the original number. Yes it is an extremely asymmetrical and imbalanced definition, but it is agreed upon so that "square root" can be a function. Functions gives only one value to each number.
So the square root of 16 is 4.
But if you define it as a multiple-valued function, it can be -4 as well. So it can depend on the context. Honestly the argument is simply a question of notation or definition, much like arguing whether the first positive number is 1 or 0. Its not really a mathematical question. On a different planet, it may very well be that the square root of 16 as a function is -4.
I would ask them to define "square root".I agree with the convention thing but say you had a test that asked you whether square root of 16 = ±4 is true or false, what would you answer? We're not talking about a variable by the way.
Ah thanks for the correction. I don't know too much about the precise definitions either. :P In that case it is true that the square root of 16 is both 4 and -4, but 4 is the principal square root.