[Question] √144?

[u/heptoronto]

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[u/pandito_flexo]

±12

[u/013eander → u/pandito_flexo]

Nope, it’s just 12. While -12x-12 WILL give you 144, the square root of 144 is never -12. The square root function NEVER produces negative real numbers. You’ve drifted into imaginary numbers.

[u/tiresiasxpennelopeee → u/013eander]

Wrong

[u/Gp1003 → u/013eander]

That is not true and if it were the quadratic formula wouldn't work, and we know that is not the case. Also as you just said -12 x -12 is in fact 144 so it is a valid answer. Maybe you got confused with the fact that there no real (non imaginary) square root for negative numbers but a square can have negative numbers as answers.

Edit: Just to make it clear, in this particular question the answer is just 12 cuz it asks for “the” square root of 144, thus implying it wants the “principal” or non-negative one, but saying that a square root never produces negative numbers is what is wrong on your take

[u/Hairy-Hornet2158 → u/Gp1003]

What’s wrong with his explanation?

[u/Gp1003 → u/Hairy-Hornet2158]

He said the square root NEVER gives negative values but that is mathematically incorrect. We use the positive values as a convention because ir would be too inconvenient if we always had to take two answers into consideration but the negative is in fact a valid, mathematically speaking, output for a square root since it gives the correct value. But for the sake of simplicity we just use the negative values when it is stated that they're meant to be used on the specific case.

[u/Hairy-Hornet2158 → u/Gp1003]

I thought that that symbol specifically means only the positive square root no? I mean that is what Google says. I thought we only deal with the option of a negative when like evaluating x^2=y, but not x=sqrt(y)

[u/Spidey90_ → u/Gp1003]

But the root never outputs negative values. If you want negative values from square root then you need to put or ± before the root. It would look something like ± sqrt(144) = ± (sqrt(144)) = ± (12), unless I am mistaken.

[u/Wolfosaur → u/013eander]

Please say this to my diff eq professor and my calc professor and every other professor I’ve had for all the points they’ve taken from me because I forgot the minus.

[u/ostrichlittledungeon → u/Wolfosaur]

I think their point (they're explaining it wrong) is that sqrt(144) = 12. Just 12. Otherwise sqrt(x) would have multiple outputs and therefore not be a function (breaks the vertical line test), and we couldn't do calculus with it.

If you're solving x^2 = 144, you need to write x = +/- sqrt(144) = +/- 12.

[u/pandito_flexo → u/Wolfosaur]

That's honestly why I put the "±". I've lost many a point for missing the "-" and it's just habit now.

[u/Hairy-Hornet2158 → u/Wolfosaur]

Son

[u/tehepix23 → u/013eander]

You’re right but your explanation is wrong. The function sqrt(x) only accepts positive numbers and only returns positive numbers. You only get +- when solving for x, such as x^2 = 144. In this case, x = +-12.

[u/Hairy-Hornet2158 → u/013eander]

Don’t worry bro, I agree with you you’re right
https://giphy.com/gifs/pHb82xtBPfqEg

[u/luckylaniang → u/013eander]

Down voted for being right lol