I don't know how to answer this question?

[dkurganov]

Hello! This is my first thread and I have a tight schedule so if for some reason this thread doesn't apply to the rules I am terribly sorry beforehand.
My question:
- so for example the square root of 16 is 4 and -4.. right? Why is it that I constantly see just one answer for problems such as [this is just a theoretical example] "find the value of... (square root 25) + (square root 9)" = and people put just "8" as the answer?? When I do the problem I think of all the possible roots: square root 25 is 5 and -5; square root 9 is 3 and -3; and shouldn't the full answer be all the possible combinations of -5/5 and -3/3? As the answer I would get 8, -8, 2, -2 as being the possible answers, but whilst checking wolphram or other sources they only get the answer of 8?
Any feedback on this question would be greatly appreciated

 

[Deleted member 4993]

Hello! This is my first thread and I have a tight schedule so if for some reason this thread doesn't apply to the rules I am terribly sorry beforehand.
My question:
- so for example the square root of 16 is 4 and -4.. right? Why is it that I constantly see just one answer for problems such as [this is just a theoretical example] "find the value of... (square root 25) + (square root 9)" = and people put just "8" as the answer?? When I do the problem I think of all the possible roots: square root 25 is 5 and -5; square root 9 is 3 and -3; and shouldn't the full answer be all the possible combinations of -5/5 and -3/3? As the answer I would get 8, -8, 2, -2 as being the possible answers, but whilst checking wolphram or other sources they only get the answer of 8?
Any feedback on this question would be greatly appreciated

This is a matter of convention. By convention:

√(25) = 5 (only positive value)

But

25 = x² → x = ± 5

 

[ksdhart2]

The difference here is a concept known as the principal root. The principal root of some non-negative real number x is defined as "the unique non-negative [nth] root of x." In other words, the principal root is always the positive root. Further, when we write \(\displaystyle \sqrt{x}\) that symbol always implies the principal root.