Math test question...Already taken it, got it wrong...WHY?

Well...it depends on how precisely this was worded. It's true that both 12 and -12 give you 144 when squared. And if we had the equation x^2 = 144, then it would have two solutions: 12 and -12.

However, when we write "√144" with the radical, it's implied that we ONLY want the positive solution. Otherwise, we couldn't consider numbers like "√144" or "√2" or "√3" to be constants.

This is because when we write actual numbers in math, there should be no ambiguity about their value. For example, it's true that the irrational numbers -2.236067... and 2.236067... both give us 5 when squared. But if I write "1+√5", then I mean "3.2360679774...", NOT "-1.23606797..." which is what we'd get if we took the negative value for √5.

Depends on how it was asked exactly. Yes it is true that the square of -12 is 144. And it is true that the solutions to x^2 = 144 are +12 and -12. But if you write 144 under a radical sign (√144) or write sqrt(144) in text like here, that notation stands for the positive square root, or 12. If you want the negative square root you write -√144 or -sqrt(144).

Think about how the quadratic formula is written.

x = [-b +- sqrt(b^2 - 4ac)]/2a

Why would we need that "+-" if the square root sign stood for two possible values already?

I see some correct answers have gotten thumbs down. This is something people will argue endlessly with working mathematicians about but that's just the way it is. By convention in mathematics, the square root sign stands for the positive root.

It depends how it was written.

If it was written with the radical (the "square root sign"), then you're actually just talking about the positive root and the answer would be 12 only.

If it was written out "Square root of 144", you have an argument for both 12 and -12 being true.

The difference is that when the radical sign is used as the square root sign, we're talking about the "principal square root function", which only has positive values.

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Now if only someone could explain to me what the principal square root of sqrt(-1) is.

;-)

it is correct., -12 x -12 does equal 144. the two negatives offset and create a positive.

your teacher is an idiot. It's both 12 and -12. You would get a mark for either if the test only asked for one

12 and -12 is the correct answer.

your teacher probably wasn't doing his or her job right. Unless you multiply both numbers with both signs (12 x (-12)) that is right. Your teacher is just not paying enough attention.

yesss....you are right...you're teacher needs to pay attention go talk to him.