Why is it called a SQUARE root?

[@domainofscience]

Hey thanks for all the wonderful comments. For those of you who pointed out that I didn't talk about complex numbers, I think you make a fair point that I could have at least mentioned them. I wanted to keep the video simple, and so decided to just ignore complex numbers, but in hindsight I think mentioning would have been good so that people who have not heard of them before at least know they exist. So thanks for pointing this out. I like finding out what you think works or not. :)

[@renpnal229]

Could you make a video explaining WHY we can solve equations and inequalities by e.g. subtracting same number from both sides? For example, 5x + 7 = 3x - 3 2x = -10 x = -5 Many people overlook this and don't understand why we can do this and why is x = -5 the only possible solution to the equation. Especially with inequalities, some have hard time understanding why the inequality sign flips when we multiply by -1. However, this is is quite simple actually. By definition, for every function f : R->R we have x = y => f(x) = f(y), and since e.g. subtracting can be thought of as a function, we can subtract from both sides of the inequality. If the function f is also an injection, by definition x = y f(x) = f(y), and the equations are equivalent. If the function f is increasing, by definition x >= y => f(x) >= f(y), and we can construct similar arguments for strictly increasing, decreasing and strictly decreasing functions. This also explains why x = -5 is the only possible solution to the equation in my example. Since, subtracting -7 can be thought of as a function f(x) = x - 7 and division by 2 can be thought of as a function g(x) = x/2, which are both injections, 5x + 7 = 3x - 3 must be equivalent to x = -5 and since x can be equal to -5 only when it is -5, x = -5 must be the only solution. This also explains why we need to be careful when squaring both sides of the equation, since h(x) = x^2 is not an injection, which may give us additional solutions, e.g x = 1 => x^2 = 1, but now also x = -1 is a solution.

[@germenfer]

If ^2 is a Square because of two dimensions, and ^3 is a Cube because of three dimensions, I suggest the following: ^1 is a Line ^0 is a Dot ^4 is a Tesseract

[@pbice]

2:40 "Just trust the math" That's all I can do in class! 😂

[@mathholica]

I have a question... Who came up with this idea? Is it your research or thoughts? I want to learn this kind of math. Thank you so much. I will wait for your reply... plz.

[@sunirainbow]

Wow. I don't know why teachers just didn't show us what you just did when explaining square roots. It makes so much sense.

[@michelferreira7488]

Square root comes from the latin origim "Radix Quadratum", which means "The side of a square". In the beginning, they used the term "Radix quadratum 16 equalis 4" or "The side of square 16 equals 4." Later they made abbreviations: "r quadratum 16 = 4" and then they jumped to "r16 = 4" and finally "√16= 4." This "√" shaped symbol is in fact a "r" alphabet letter. A shortcut notation that is. "Radix" in latin based language was wrongly translated to "Raiz" (because the phonetics of the words are very alike) which means "root" in English language. The correct translation term should be "Side" ("Lado" in latin based languages), not "raiz". So, square root means "the side of a square side 16 is equal 4". I hope that helps.

[@hamrogarage4658]

You mean side of 16 area square is 4

[@mjptbcwreisnarsapurattoopr3837]

Tq

[@Enzoerb]

thanks, it helped a lot, I was wondering about the "ROOT" because i speak portuguese and it is the literal translation of "RAIZ" that is how we call it here, so i was thinking "What a tree root has to do with numbers, it is a tree of numbers?" then u answered it to me.

[@Time4yes]

So are you saying, the need of a square root is to find the value of side(s), depending on the shape?

[@conservativepatrick]

Perfection.

[@syazanizulkhairi8918]

hey man, nice video.. this is exactly what students need this days.. I love videos like this that focus more on understanding than just following and memorizing .. you're teaching real math man keep it up

[@domainofscience]

Hey thanks so much for your really nice comment! And yes, that is totally my goal - I have no idea why they didn't tell us this in school. Great to know you think this kind of thing is valuable.

[@Szobiz]

Syazani Zulkhairi much better when things make sense, right?

[@popcap990]

I agree with your comment man

[@vishnurajput334]

No 😊😊😊

[@truthseeker7815]

@@vishnurajput334, yes 😈😈

[@MikeRichman]

No love for imaginary numbers? ;-(

[@voiceinthevoid14]

√(-1) like them. haha see what I did there? and yes I have no friends.

[@TourmalineHealer]

Tristan Scott I'll be your friend

[@Ardkun00]

i

[@manda3dprojects966]

iGirl = imaginary girl

[@manz007]

iota

[@andresbarriga5305]

Keep up the good work. This is the kind of channels we need.

[@lontongtepungroti2777]

yes

[@hansanikularatne5287]

Exactly!

[@illbet4589]

I always wondered this but none of my teachers would ever give me a good and straight answer! Thank you for this video!

[@sorvex9]

Cause they didnt know

[@tanoherc1]

Nice video. I may only say that at the level of real numbers the square root function is defined to always take the positive choice: e.g. the square root of 25 is 5, not -5. A completely different thing is to find the roots (or zeros) of the polynomial x^2 - 25: in that case you have 5 and -5. Perhaps the similarity of the notions (and the words used to denote them) is a little confusing a priori, but they are indeed different things. Best.

[@predicate]

was looking for this

[@Firefly256]

Ah yes, x^2 - 25 has a solution without the equal sign

[@justyourfriendlyneighborho2061]

I was looking for this comment

[@darchcruise]

I wish this KZbin channel existed when I was in school. I love it!

[@franjocilic2694]

Me as well...

[@95BWG]

The part about a square root being either negative or positive is false. The square root of a number is always positive, which is why the solution to x^2 = 4 is x = +/- sqrt(4) = +/- 2 - the square root of a number is defined as the positive solution to this type of equation. So if you take a number, square it and then take the square root of it you get the absolute value of that number.

[@annieyu4490]

No, that's not how it works, I was taught that square roots can be any number.

[@95BWG]

I guess it's a matter of semantics, but it's definitely true that sqrt(x^2) always gives you a positive number.

[@theworriedbeaver33]

You're correct, it is a matter of semantics. In the video at 1:45 what he says is tecnically correct, but what he writes is wrong. 'Square root' can mean different things. When you write √16 you do not refer to all square roots of the number 16. You only refefer to the 'principal square root', or the positive one. This is because a function can only output one object so people had to restrict the general concept to make it a function. In this case √ is a function from R+ to R+. At 1:47 he says 'people noramlly just take the positive'. This is very very wrong as math is not an opinion, there has to be a good reason to pick +4 over -4. And the good reason is: that is the definition. There are other cases when √ means other things, this is usually clear from the context, like √-16 does clearly not refer to the same function as above. There are even different situations where people write √z where z is a complex. Here √ is not even a function, it's just a fast way to write 'all square roots of z'. Now you could argue that √16 is also a conplex with immaginary part = 0, but unless it's explicitly clarified the standard √:R+ -> R+ should be always assumed. There are enormous misconceptions around square roots, and you're right it's a matter of semantics, unfortunately we use the same words for all the cases.

[@95BWG]

The worried beaver Thank you for a clarifying and well-formulated reply, the likes of which you do not often get on KZbin. Appreciate it!

[@Paraselene_Tao]

To mitigate this confusion it's best to say, "the principle square root" of x. This gives us an always positive number

[@atishmistry6959]

Big love from a maths teacher in the UK. I'll be showing this to my class!

[@JW-bc4uq]

Rock On! I NOW HAVE MY LIFE BACK; I was mulling over this one in my grey matter for a few weeks and none of the reference books made it understandable for me. I finally I got it in three minute. Thanks.

[@sebastianchem978]

Dominic your videos are amazing. Please don't stop making them. I'm sure one day your channel will have millions of subscribers because your videos are just so good.

[@venkatkotti]

You are a genius. I love those graphics. Excellent!!!!

[@markptak5269]

Nice job however I suggest some nod or mention to the fact that one can't take the square root of a negative number only when you confine yourself to the real number system.

[@danandrews2175]

Wow. Your depiction of the fourth dimension is going to influence how I imagine it from now on. I doubt my teachers even knew this to be honest... in fact, my brother's a teacher, so I'm going to ask him if he knows (I bet he'll just make something up).

[@EnergiaRocket]

It... was not a real depiction. Those base vectors weren't linearly dependent since it is a two-dimensional depiction of a three-dimensional depiction of a four-dimensional object.

[@legitgopnik8431]

I think he was being sarcastic, Org.

[@ahmednaser6850]

actually, what I know is that the symbol of square root is coming from the Arabic word جـذر which means "root" and the first letter of it جـــ is that symbol of this operation since the inventor of it is al khawarizmi and he speaks arabic

[@akshnarwani8803]

This is called pure knowledge. Teaching mathematics with the real logic not only using random numbers to show what a thing is.

[@jonathanespach7876]

I think I was on planet Mars when my maths teacher discussed this with the class.. I love your work mate.

[@hammadrasool2398]

Genius bro! That's the maths I wanted to learn at school.

[@Thedigitalalex]

I am so grateful to you . I had never understood this my whole life.

[@fatemehhussaini6535]

Thank you so much you explained more than everything I needed to know! Good work.

[@Tymon0000]

N√(-1)ce V√(-1)deo

[@mohammedasadi]

I wish you were my math teacher! I'm 36 years old and this is the first time ever I understand it. Thank you

[@Bicho04830]

I spected a explain for the "root" word

[@eddyfirdeus1]

You are amazing, I have struggled so long and never understood those things, you explain things so beautiful and all that with visualizations. Thank you so so much and please keep going making such wonderful explanations.

[@JohnZyski]

This was incredibly useful and informative. Thank you.

[@siroggak]

So I understood "square" part (thank you for that!), but what about the "root" part? Why is it called "square ROOT"? Btw, interesting depiction of tesseract. All those pictures on the internet don't give you any clue about what it actually looks like, they only lead to confusion. And you came up with your own solution, that's cool! :)

[@dragonzed]

I knew where the "square" part comes from, and came expecting an explanation of the "root" part, but even you mention it at the end I still have to ask ¿what is the meaning of the word "radix" in roman? :P This needs an answer!

[@dragonzed]

Also, it would be nice to know where does the symbol comes from.

[@panoskaoukis7668]

Please correct me if I'm wrong! In the video you said that a perfect square is a number that it's square root equals a whole number ! My question is : Is 0,01 a perfect square ? Because its square root equals 0,1 (not a whole number but neither an irrational number)

[@priyankasingh-ho9ww]

I am searching for physics content and I got yours and you are amazing.👍

[@warshipproductions5059]

Wow I learned more about square roots in this video than in my 22 years of existence

[@jaymishra7560]

Man you deserve more than 1M subscribers ! Great work, always love your work

[@russellharris1299]

THAT'S WHAT I NEEDED TO KNOW , now i can visualise what I'm trying to work too!!!!!!!!

[@tanweercaa]

Excellent, beautiful. Maths needs to be loved if taught like this.

[@avi12]

2:32 I love this 4th dimension representation

[@workout9594]

Root16 is NOT +-4, you take the absolute value only so it is +4

[@abdulrahmanansari7433]

Better understanding of the roots give you better command on offshoots. Thanks for the explanation 👍

[@RafidW9]

I absolutely love your videos. and I saw your ted talk on KZbin which wonderful. keep making these videos, we really love them and need more of them!

[@Omar-vz9el]

Thank you for videos like this! I fucking hate how in high school and even college we are stuck just plugging and chugging without being told what all this means. Insight to these things really help understand why they come in to play in mathematical equations. That explanation of 4^3 was amazing and how it stands for three dimensions was completely unknown to me!

[@sciencedon3993]

Your way of teaching is incredible.

[@ivonnepresley8051]

Dude, your videos rock! Keep up the awesome work 😁

[@ConservativeHippie001]

I have been wondering this since I was a kid. Thank you! Excellent video!

[@weststarr2046]

All your videos aré AMAZING focusing on really understand the subject. THANKS a lot. One subscriber!

[@WalterUnglaub]

Very lovely animations! Keep up the good work!

[@Ive03]

Great explained

[@pankajagrawal7338]

Thx for this I was searching whole yt to find this explanation and only this video was there so thx

[@hishammubarak3421]

The 3 minutes was worth it!

[@damagineer3147]

That part at the end was what I was waiting for. I knew the square part just not the root part.

[@draconyxRPG]

I learnedcthat square root of 16 is 4, not -4. But x², x = +-4.

[@travelingmerchant6931]

I've been studying this throughout the night. Ever thought, why is there only a "square" root? What about a triangular root? A circular root?

[@AAMEERAHMARIANO]

This is more than I learned at school. Thank you, friend.

[@Nabiyah1]

Thank you. Great Simplistic Video. Straight to the point.

[@Shanmuganathan2316]

i am wordless.Can someone explain a conventional term's reason so easily?Man u r awesome

[@pharathcheam1869]

Wow dude that is so easy to understand

[@spacebatstuckonearth8888]

Damn dude dat explanation was clear as hell. Keep it up the world needs it

[@Reino_X]

I know a solution to this problem with negative square roots. There just has to be a different square root which basicly takes 2 of the same number and adds 1 positive and 1 negative of it and multiplies them. That's how you get a negative number after all! It would basicly be the same as the square root we have now but a bit different...

[@1anya7d]

I really love your channel, what are you planning to upload next?

[@taseti3607]

Subscribed. Simple and visually entertaining.

[@mactavish6236]

wow man! I wondered all through the time since I studied square root and cube root that why what any number to the power a fraction would actually look like ??........ This video gave me clarity, not 100%, but yeah it gave me some. Thanks Dominic.

[@pbezunartea]

You dodged complex numbers! ... and they are not imaginary! ;) Great video!

[@sakornsaokaew9391]

I hate mathematics but I love this.

[@arifkizilay]

hi, thank you so much. almost perfect explanation. I asked one of the math channels these questions. I think you answered them partially. I will check your other videos to see if you have more explanation about the square root. I wonder why they have come up with the idea of square root. What part of math it solves. why do we need square root? Is it only a mental satisfaction? Why do we need to know square root? What are we trying to solve by knowing square root? thank you.

[@annellen2694]

Wow ! I learned sm! Thank youuu

[@renesingson8142]

The editing and animation of these videos is really cool, like that of the 4D hahaha

[@vegavisiaai2321]

Great and informative.. Your teaching skill is really amazing.. Keep it up My Friend... You're doing Great to many people.. Love you Brother

[@kc1442]

@Domain of science Thank you so much for explaining this with so much detail. I have always struggle with math, mainly because I haven't been able to understand the concept of it, nor the meaning of things like this. I know understand this because of your explanation. Are you available for online math tutoring?

[@NicholasJeffery]

Enlightening! Thanks!

[@chencw-math]

The word "root" has been used since ancient Greek's era. Together with the word "power", they were both derived from Aristotle's terminology. In Aristotle's philosophy, a segment has an inner potential (translated to "power" in English) to realize itself so that it becomes a square region, like a seed grows up to be a tree. That is the reason why a side is called a root of a square. This also explains why the mutiples of numbers are called powers. :-)

[@sebaalge6674]

thanks

[@manjusherawat6115]

Hay bro that is the quality content Your thinking is at the another level very good

[@cubism_2]

Am I the only one who refers to the fourth power as “tesseracting”? Since the 2nd power is a square, and the third power is a cube, doesn’t it make sense that the fourth power is a tesseract?

[@motherof3pearls]

Thank you! I’m loving it! 🤓

[@null1449]

Wow, well explained, greetings from Ecuador

[@kee1zhang769]

I learnt that Johannes Müller von Königsberg (better known as Regiomontanus) invented a symbol for a square root, written as an elaborate r, in 1450AD

[@ivisionaries1.618]

Great teacher 👍

[@I_Echion]

Your videos are so well made

[@KeyMan137]

Why no mention of the complex numbers?

[@chumsky8754]

Math is a beautiful collection of related things. he wonderfuly explained square roots for positive integers. If someone wanted to understand that, they have been given a great introduction. If someone actually thougt hard and wondered "what about negative integers?" that would be great mathematical thinking and such a motivated person would have no trouble finding the answer in another youtube video or wikipedia (or, God forbid, a library and books). If they were familiar with complex numbers, they would probably be fine with the square roots of positive integers.

[@evab1410]

In Dutch, we call a root a 'wortel' which means carrot or (well..) root. So if you want to know the square root of 4, you calculate the carrot of 4. And I never knew why we just literally translated it instead of making a new and more logical word..

[@trex4561]

Sir deeply respect from Himalaya mountain .

[@eryntodd]

Thank you for the very informative video! Also if anyone knows; what's the name of this background song? it sounds like a instrumental/acoustic

[@dr_drw]

This is so awesome! How did you make the 3D animation?

[@MrTraiq]

Very well explained! Thank you

[@EnergiaRocket]

Well... It is kind of obvious. I would enjoy the origin of the word 'root' more. I mean like in, more than at the end of the video.

[@lyall3000]

Thanks for the video. At 2.00-2.15, isn't it fair to say that the argument we can't have a square root of a negative number is simply a convention we've decided upon, rather than any mathematical necessity. As you can see at 2.12, both 4x-4 and -4x4 both yield an absolute area of 16 on a 2D plain, just like 4x4 and -4x-4. So why is it inaccurate so say you can't get an area of 16 or -16 (depending on whether your dealing with absolute areas or not) by multiplying 4 x -4? It makes perfect logical sense that you could - you have -4, and you increase that by a factor of 4, so now you have -16. If negative integers exist, why can't negative areas? It's like we've just decided we can have negative numbers in one dimension (a theoretical construct), but we've decided you can't have negative areas in 2D. I'm not a mathematician and I'm sure there is a good explanation, but it isn't obvious. Also, isn't there a theoretical inconsistency in not putting the bottom LHS quadrant in the top RHS quadrant. Logically it would seem 4x4 =16 with a positive area in two dimensions. -4x4 and 4x-4 is an absolute area of 16 that is negative in one dimension and positive in another, and -4x-4 is an area of 16 that is negative in two dimensions. If we are going to say negative areas are impossible, which we are in disallowing a square root of -16, then why are we able to have an area of -16 shown in this quadrant that is negative in two dimensions. To a casual observer, it seems like we are just tying ourselves in knots because we are trying to come up with operations in multiple dimensions while insisting we can only have negative numbers in one dimension, which doesn't make a lot of sense to me.

[@tasteful_cartoon]

Everything good until you said √16=±4

[@polysopher]

In geometry, to sum 2 point you have to square them first, add them and finally sq root give you the value. C2 = a2 + b2

[@youlittlefat]

The origin is from latim "radix quadratum 16 aequalis 4" that can be translated to "the side of square 16 is 4"

[@johnjohnson3457]

The square root is by definition the positive root.

[@tarunreddy6591]

mind blowing animation design....congo to your animation team

[@Steve_Thompson]

Well done. Great explanation.

[@ornessarhithfaeron3576]

Complex plane: Am I a joke to you?

[@bheemsinghnenavathnenavath6131]

Nice explanation

[@alanmc9660]

Thanks for sharing 👍

[@googleplex1589]

Do you know why plants hate math? Because it gives them SQUARE roots!!! 🤣🤣🤣

[@annymainframe3216]

Thanks, was very interesting and educational

[@martamanassero3303]

Nice video, but it is never mentioned that not perfect square roots are irrational numbers. The word used is "decimal" that's quite generical and the number show seems to have a finite decimal part without the "..." . So a root can be whole or irrational: it's something in my opinion (ask Pythagoras for more details ;) )

[@ITsmapleTimexD]

Great video! Keep it up!

[@nakhanwazir7193]

Sir why the radical sign is equll to 1÷2

[@alexcordero6672]

Oh my God.. Thank you so much for explaining this. I've been trying to get an answer to this and nobody knows what I'm asking. I know how to do all sorts of things using square roots but they're all arbitrary little number games with seemingly no meaning at all--just another grade to get in a class. This video ads dimension to this concept.