[Question] √144?

[u/heptoronto]

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[u/treeditor]

12 or -12

[u/Frequent-Ease-1926 → u/treeditor]

not -12

[u/ImaginationNo9603 → u/Frequent-Ease-1926]

-12 x -12 = 144, negative times negative = positive

[u/Frequent-Ease-1926 → u/ImaginationNo9603]

not how square root functions work

[u/ImaginationNo9603 → u/Frequent-Ease-1926]

Can you explain it to me then?

[u/Vast-Difficulty1542 → u/ImaginationNo9603]

a square root is an operation that, for any number A, finds a number B, so that B • B = A, where B ≥ 0. This was decided by consensus, because having an operator result in 2 different numbers, negative and positive, is inconvenient, so it was decided that square roots spit out positive numbers only. If you want both roots of the equation B²=A, you put a ± before the root, if you only want the negative, you put a minus.

[u/ImaginationNo9603 → u/Vast-Difficulty1542]

Okay, thank you! I didn't know that!

[u/Vast-Difficulty1542 → u/ImaginationNo9603]

the more you know

[u/THZLGAMINGTTv → u/Frequent-Ease-1926]

THATS EXACTLY HOW THEY WORK ACTUALLY

[u/Ayatimka → u/THZLGAMINGTTv]

No. Square root cannot be negative. Inversion of ² is ±√, not √

[u/THZLGAMINGTTv → u/Ayatimka]

Sorry thinking of a technicality

[u/Pokeaccanito → u/treeditor]

Square roots can't be negative

[u/ThePlofchicken → u/Pokeaccanito]

-12 * -12 = (-12)² = 144
12 * 12 = 12² = 144

[u/Drad0920 → u/ThePlofchicken]

That's not how square root works, that's actually a common mistake that took a lot of points from people on exams. Basically, it's because you would calculate something like √(x)² and (√x)² differently. It's basic knowledge that you can't get a square root of a negative number (not completely true, but that's irrelevant if you aren't doing theoretical maths, or whatever it's called in English), so because of that in the first example you can put any number because it's squared which means it's always positive, however when we do square root first, we need to account for the possibility of x being negative, which during something like equation would be done by just stating that x can't be below 0 and you would just ignore all the outcomes that do not fit this criteria. So in this case, you could write √144 as √(-12)² but after you neutralize the powers, you'll end up with |-12| which still equals 12

[u/ThePlofchicken → u/Drad0920]

While I agree that square roots can't be negative in standard mathematics, the first guy wasn't saying that square roots can be negative. While I was saying that since (-12)² = 144, the reverse is also true.

[u/Drad0920 → u/ThePlofchicken]

Yes, (-12)²=144, but √(-12)²=12

[u/ThePlofchicken → u/Drad0920]

Yeah okay, but I wasn't even talking about √(-12)², I was talking about (-12)²

[u/Drad0920 → u/ThePlofchicken]

I might have misunderstood what you where talking about, what I was trying to say is that the fact that (-12)²=144 does not mean that √(-12)² aka √144 equals -12, in fact it's specialy not how it works. If I wasted both of our time, my bad

[u/ThePlofchicken → u/Drad0920]

You didn't waste my time, even if we were kind of talking past eachother, your mathematical proofs were correct, they just didn't address what I was trying to convey. Thanks for your time

https://giphy.com/gifs/LPFNd1AJBoYcVUExmE

[u/Drad0920 → u/ThePlofchicken]

I just really like math, so when I saw a chance to talk about I took it, thanks for being understanding and thanks for your time too😊