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.
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.
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. :)
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.
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
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.
Idk why teachers acted like they weren’t reteaching themself with the same video the night before then they roll their eyes you can’t get it it the next day 😂
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
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.
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.
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.
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.
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.
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.
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.
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)
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
It's understandable why you might associate Al-Khwarizmi with the square root symbol, given his foundational contributions to algebra and mathematics. However, the square root symbol (√) as we know it today was not invented by Al-Khwarizmi. Al-Khwarizmi (circa 780-850 CE) was an influential mathematician from the Islamic Golden Age, and his work, particularly his book Al-Kitab al-Mukhtasar fi Hisab al-Jabr wal-Muqabala (The Compendious Book on Calculation by Completion and Balancing), is considered one of the key texts that helped lay the foundation for algebra. In his work, Al-Khwarizmi dealt with solving quadratic equations and square roots, but he used words and geometric methods to express these concepts-he did not use the radical symbol. The actual square root symbol (√) was introduced much later, in the 17th century, by Rene Descartes in 1637. Descartes used the symbol in his work La Géométrie, making it more widely recognized and standardized in mathematical notation. Al-Khwarizmi's contributions were indeed critical to the development of algebra, and his name is the root of the word "algorithm," but the square root symbol itself came much later with Descartes.
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).
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.
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.
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!
1:27, that is wrong, the square root gives only positive numbers. So, sqrt(16) is only 4. That is why the equation: sqrt(x)=-2 has no solution. If you don't believe me, put it in WolframAlpha
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! :)
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.
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!
Sorry about my question but, if I say y= x², do I mean area=x², why does it become a parabola? or am I talking about the area of parabola? please answer
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.
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. :-)
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.
@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?
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...
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.
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..
![Imaginary Numbers Are Real [Part 1: Introduction]](http://i.ytimg.com/vi/T647CGsuOVU/mqdefault.jpg)
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.
You mean side of 16 area square is 4
Tq
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.
So are you saying, the need of a square root is to find the value of side(s), depending on the shape?
Perfection.
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. :)
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.
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
2:40 "Just trust the math" That's all I can do in class! 😂
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.
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.
Theu have to justify their jobs....
Idk why teachers acted like they weren’t reteaching themself with the same video the night before then they roll their eyes you can’t get it it the next day 😂
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
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.
Syazani Zulkhairi much better when things make sense, right?
I agree with your comment man
No 😊😊😊
@@vishnurajput334, yes 😈😈
No love for imaginary numbers? ;-(
√(-1) like them. haha see what I did there? and yes I have no friends.
Tristan Scott I'll be your friend
i
iGirl = imaginary girl
iota
Keep up the good work. This is the kind of channels we need.
yes
Exactly!
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.
No, that's not how it works, I was taught that square roots can be any number.
I guess it's a matter of semantics, but it's definitely true that sqrt(x^2) always gives you a positive number.
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.
The worried beaver Thank you for a clarifying and well-formulated reply, the likes of which you do not often get on TH-cam. Appreciate it!
To mitigate this confusion it's best to say, "the principle square root" of x. This gives us an always positive number
I always wondered this but none of my teachers would ever give me a good and straight answer! Thank you for this video!
Cause they didnt know
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.
was looking for this
Ah yes, x^2 - 25 has a solution without the equal sign
I was looking for this comment
I wish this TH-cam channel existed when I was in school. I love it!
Me as well...
Big love from a maths teacher in the UK. I'll be showing this to my class!
I think I was on planet Mars when my maths teacher discussed this with the class.. I love your work mate.
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.
You are a genius. I love those graphics. Excellent!!!!
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.
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.
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)
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
It's understandable why you might associate Al-Khwarizmi with the square root symbol, given his foundational contributions to algebra and mathematics. However, the square root symbol (√) as we know it today was not invented by Al-Khwarizmi.
Al-Khwarizmi (circa 780-850 CE) was an influential mathematician from the Islamic Golden Age, and his work, particularly his book Al-Kitab al-Mukhtasar fi Hisab al-Jabr wal-Muqabala (The Compendious Book on Calculation by Completion and Balancing), is considered one of the key texts that helped lay the foundation for algebra. In his work, Al-Khwarizmi dealt with solving quadratic equations and square roots, but he used words and geometric methods to express these concepts-he did not use the radical symbol.
The actual square root symbol (√) was introduced much later, in the 17th century, by Rene Descartes in 1637. Descartes used the symbol in his work La Géométrie, making it more widely recognized and standardized in mathematical notation.
Al-Khwarizmi's contributions were indeed critical to the development of algebra, and his name is the root of the word "algorithm," but the square root symbol itself came much later with Descartes.
This is called pure knowledge. Teaching mathematics with the real logic not only using random numbers to show what a thing is.
I spected a explain for the "root" word
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).
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.
I think he was being sarcastic, Org.
Your way of teaching is incredible.
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.
I am searching for physics content and I got yours and you are amazing.👍
Genius bro! That's the maths I wanted to learn at school.
Thank you so much you explained more than everything I needed to know! Good work.
This was incredibly useful and informative. Thank you.
I wish you were my math teacher! I'm 36 years old and this is the first time ever I understand it. Thank you
Man you deserve more than 1M subscribers ! Great work, always love your work
I am so grateful to you . I had never understood this my whole life.
Sir why the radical sign is equll to 1÷2
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!
Also, it would be nice to know where does the symbol comes from.
1:27, that is wrong, the square root gives only positive numbers.
So, sqrt(16) is only 4.
That is why the equation: sqrt(x)=-2 has no solution. If you don't believe me, put it in WolframAlpha
Wow I learned more about square roots in this video than in my 22 years of existence
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! :)
Better understanding of the roots give you better command on offshoots. Thanks for the explanation 👍
Why no mention of the complex numbers?
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.
Very lovely animations! Keep up the good work!
Subscribed. Simple and visually entertaining.
All your videos aré AMAZING focusing on really understand the subject.
THANKS a lot.
One subscriber!
Can you make us understand the square root of 2 in the way you find the square root of 20 by using one of its side? @ 1:11
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
I absolutely love your videos.
and I saw your ted talk on TH-cam which wonderful. keep making these videos, we really love them and need more of them!
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?
I have been wondering this since I was a kid. Thank you! Excellent video!
I really love your channel, what are you planning to upload next?
2:32 I love this 4th dimension representation
Excellent, beautiful. Maths needs to be loved if taught like this.
Thank you. Great Simplistic Video. Straight to the point.
What is a number multiplied by 4 called and what is the inverse of it called?
Hay bro that is the quality content
Your thinking is at the another level very good
What’s to stop there being a fifth, six, seventh, etc dimension?
√-16 = 4i
Root16 is NOT +-4, you take the absolute value only so it is +4
Your videos are so well made
Great teacher 👍
Damn dude dat explanation was clear as hell. Keep it up the world needs it
Thx for this I was searching whole yt to find this explanation and only this video was there so thx
Great explained
Wow, well explained, greetings from Ecuador
Great and informative.. Your teaching skill is really amazing.. Keep it up My Friend... You're doing Great to many people.. Love you Brother
This is more than I learned at school. Thank you, friend.
This is so awesome! How did you make the 3D animation?
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!
Wow ! I learned sm! Thank youuu
Sorry about my question but, if I say y= x², do I mean area=x², why does it become a parabola? or am I talking about the area of parabola? please answer
Thank you! I’m loving it! 🤓
N√(-1)ce V√(-1)deo
i am wordless.Can someone explain a conventional term's reason so easily?Man u r awesome
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.
THAT'S WHAT I NEEDED TO KNOW , now i can visualise what I'm trying to work too!!!!!!!!
The 3 minutes was worth it!
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. :-)
That part at the end was what I was waiting for. I knew the square part just not the root part.
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.
Is there a similar graphic explanation where you can use the imaginary numbers and the complex plane to show there's a solution to sqrt(-1)?
not visually, our brains are limited
I hate mathematics but I love this.
@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?
mind blowing animation design....congo to your animation team
Wow dude that is so easy to understand
Well done. Great explanation.
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...
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.
Very well explained! Thank you
Is the forth dimension time?
You r what simplicity is made of! Thank you😂😂😂😂😂😂😂😂😂😂 2 neat!
I learnedcthat square root of 16 is 4, not -4. But x², x = +-4.
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
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..
Enlightening! Thanks!
Great video! Keep it up!
The editing and animation of these videos is really cool, like that of the 4D hahaha
What are some useful applications for the square root?
You dodged complex numbers! ... and they are not imaginary! ;)
Great video!
thanks
Nice explanation
I love it Sir ! A greaaaaaat concept Ever ..... Love it !!!
Thanks, was very interesting and educational
Thanks for sharing 👍
why than we never take -4 for 16 under the root of 2 ???