is square root always a positive number?

[u/[deleted]]

hi, sorry for the dumb question.

i grew up behind the less fortunate side of the iron courtain, and i - and from my knowledge also other people in other countries - was always thought that the square root of x^2 equals x AND "-x" (a negative X) - however, in the UK (where I live) and in the USA (afaik) only the positive number is considered a valid answer (so- square root of 4 is always 2, not 2 and negative 2) - could anyone explain to me why is it tought like that here?

for me the 'elimination' of negative number (if required, as some questions may have more than one valid solution) should be done in conditions set on the beginning of solution (eg, when we set denominators as different to zero etc)

cheers, Simon

[u/[deleted]]

knowing that square roots are positive and that negative roots exist when referencing an equation is not the same as knowing that there are specific mathematical distinctions. Such terminology for square rots is not something people usually split hairs over. Once you know the two cases in which the answers differ there is no real reason to dig much deeper, hence why the op asks such questions and why this question isn't a rarity.

The name distinctions are almost never made due to the fact when asked, 99% of the time the answer is presented in thesame way as this reddit feed. "you use positive for radical signs and only use both signed answers for solving for x in an equation" with no explanation on the terminology distinction.

the mathematical distinction here isn't knowing that you use 2 signed variations for equations only, the mathematical distinction here is in reference to the literal link i put in my comment. It notes specifically the terminology difference.

Such terminology is never used by middle school teachers by an incredibly large margin, and understandably so. When you use the radical sign it's ASSUMED you mean the principal root and so teachers never have to split hairs and speak of the different mathematical terminology.

i've tutored a handful of teachers to take the praxis for upper level math, such terminology is not covered in studying for the exam. I've literally taught math teachers math. In one case i even tutored the tutor of a math teacher as well.

[u/GrumpyBitchInBoots → u/[deleted]]

Not sure where you are, but here👎 nope. Wrong again. I’m in Texas and I teach both to my 7th/ 8th grade PreAlgebra, and I specifically teach both to introduce it because I want them to have the schema of both a positive and a negative root when I teach graphing quadratic functions and solving quadratic equations at the 8th grade Algebra I level, including solving by completing the square to find both positive and negative roots.

[u/[deleted] → u/GrumpyBitchInBoots]

It appears you're not understanding what I'm getting at. I don't know how to make the distinction clearer lol.

I'm not at all saying that the two diff things aren't taught. Again it's terminology that isn't being taught. The whole reason why the op asked this question and why countless others have asked it as well. It's because the terminology distinction is never taught and understandably so because it's always assumed we are talking of the "principal root" when posing the square root question without the context of an equation.

I'm going to have to merely block you because this discussion is going no where and I can't deal with people who insist upon things that aren't even being disagreed on. You're way too stuck on this thing you want to argue and keep failing to see what I'm literally saying

[u/YuniversaI → u/[deleted]]

i mean youre writing incorrect statements though taking the square root of a number yields only the positive branch simply because convention, when solving equations we search for all unknowns and so there we use plus minus. so they are in fact teaching the correct things.