here's the deal: you're talking about two different things.
when you have an OPERATOR SYMBOL, such as "√", that symbol will produce exactly ONE value.
for instance, √9 is just 3.
|-5| is just 5.
and so on.
notice, in these cases, that you're merely simplifying expressions; you are NOT solving EQUATIONS. in other words, there's no "=" sign in the middle of what you're dealing with; you're not finding the solutions of anything. just simplifying.
when you solve an EQUATION, there may well be more than one solution.
if you say x^2 = 9, there are two solutions: x = 3 and x = -3.
notice that i can say this without speaking of the "√" symbol at all!
indeed, the "√" symbol is DEFINED to refer only to the positive root. it is NOT defined to refer to either of the 2 solutions to the above equation.
hth.
Ron has been teaching various standardized tests for 20 years.
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