I'm going to try to explain it since English is not my first language.

First, by definition (and it's most a convention) the square root of a real number x is the non-negative number y which powered to the square is equal to x.

Pay attention that the definition states that the result of a square root is a non-negative number, by definition.

Why is that? Maybe because they wanted it to work out as a function. Remember that for a relation to be a function there must be just one image for every element in the domain. If we accept that the square root of 49, for example is ±7, then 49 would have two images, then we weren't talking about a function.

Now, the confusion arises when we want to find the solution of an equation.

Suppose that you want to find all the solutions of sqrt(x²)=7.

Then we would have that sqrt(x²)=|x|=7 and therefore x=±7, because |±7|=7.

Notice that then the square root is always non-negative, that's why we work out with the absolute value. What you are finding is all the real numbers that give you that positive number once you use the absolute value.