Question

When working with the square root of a number, when would you have only a positive answer and when would you have both a positive and negative answer?

Answer 1

You would have a positive answer when the value you are looking for has to be a positive number (like a real life answer such as length, width, depth, height etc.)

You would have a positive and a negative answer when you take the square root of something that doesn't have to be positive (like when you are finding a root on a graph or something of that sort that could be negative), it could be either because when a negative number is squared it becomes positive and when a positive number is squared it stays positive as well.

Answer 2

To be clear though, this symbol \[\sqrt{16}\] means only one thing: the non-negative number x which when squared is 16.

I.e., the \[x \geq 0 \ \ \text{such that} \ \ x^2 = 16\]
and that number is x = 4.

Hence the square root symbol when it is defined gives one number only.

A different problem is this: for what real numbers is
\[x^2 = 16\]
then there are two such numbers, x = 4 and -4.

Combining these two ideas,
\[x^2 = 16 \implies x = \pm \sqrt{16} = \pm 4\]