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.
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.
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.
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.
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.
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!
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.
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)
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! :)
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
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.
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.
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.
@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?
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. :-)
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..
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
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.
In Brazil we have a Math Museum with a very famous teacher that teach showing us how the math was built and all you said I have learned there yet. He has lots copy of math's originals writings so he can emerge the student in the discussions make then learn much better. He course is so famous here that others doctors in math do his course.
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....
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!
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.
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
I wish this UA-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!
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.
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.
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.
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.
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.
I am so grateful to you . I had never understood this my whole life.
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)
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! :)
Thank you so much you explained more than everything I needed to know! Good work.
Your way of teaching is incredible.
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
Better understanding of the roots give you better command on offshoots. Thanks for the explanation 👍
I absolutely love your videos.
and I saw your ted talk on UA-cam which wonderful. keep making these videos, we really love them and need more of them!
I am searching for physics content and I got yours and you are amazing.👍
I think I was on planet Mars when my maths teacher discussed this with the class.. I love your work mate.
I wish you were my math teacher! I'm 36 years old and this is the first time ever I understand it. Thank you
This is called pure knowledge. Teaching mathematics with the real logic not only using random numbers to show what a thing is.
Dude, your videos rock! Keep up the awesome work 😁
N√(-1)ce V√(-1)deo
I have been wondering this since I was a kid. Thank you! Excellent video!
Very lovely animations! Keep up the good work!
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.
I really love your channel, what are you planning to upload next?
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.
THAT'S WHAT I NEEDED TO KNOW , now i can visualise what I'm trying to work too!!!!!!!!
Thx for this I was searching whole yt to find this explanation and only this video was there so thx
Thank you. Great Simplistic Video. Straight to the point.
Wow ! I learned sm! Thank youuu
Hay bro that is the quality content
Your thinking is at the another level very good
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...
Great teacher 👍
Wow I learned more about square roots in this video than in my 22 years of existence
This is more than I learned at school. Thank you, friend.
Great and informative.. Your teaching skill is really amazing.. Keep it up My Friend... You're doing Great to many people.. Love you Brother
That part at the end was what I was waiting for. I knew the square part just not the root part.
Enlightening! Thanks!
Your videos are so well made
Sir why the radical sign is equll to 1÷2
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.
I learnedcthat square root of 16 is 4, not -4. But x², x = +-4.
Thank you! I’m loving it! 🤓
@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?
Is the forth dimension time?
What’s to stop there being a fifth, six, seventh, etc dimension?
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. :-)
Very well explained! Thank you
Thanks for sharing 👍
loved it, could you do the same for others math concepts ?
I hate mathematics but I love this.
i am wordless.Can someone explain a conventional term's reason so easily?Man u r awesome
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?
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..
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
What is a number multiplied by 4 called and what is the inverse of it called?
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
mind blowing animation design....congo to your animation team
The 3 minutes was worth it!
Thank you.
The editing and animation of these videos is really cool, like that of the 4D hahaha
If anyone is interested Wikipedia has some awesome animations of a four dimensional cube it’s called a tesseract !
√-16 = 4i
luv u sir helps a lot
What are some useful applications for the square root?
Super, thank you
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.
Why do we need negative numbers or negative space even in graphs
You r what simplicity is made of! Thank you😂😂😂😂😂😂😂😂😂😂 2 neat!
You dodged complex numbers! ... and they are not imaginary! ;)
Great video!
Thanks, was very interesting and educational
loved it !
Good job 👍
Good video!
I love it Sir ! A greaaaaaat concept Ever ..... Love it !!!
Great video! Keep it up!
Wow ... Loved it ... Thank you so much ..
How did the word radix come about ?
In Brazil we have a Math Museum with a very famous teacher that teach showing us how the math was built and all you said I have learned there yet. He has lots copy of math's originals writings so he can emerge the student in the discussions make then learn much better. He course is so famous here that others doctors in math do his course.
Complex plane: Am I a joke to you?
I am not a math geek ! But I believe that square root of -16 is not error but have an answer : 4i or -4i
I kinda guessed this but jolly interesting all the same. 👍
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
Nice explanation..... I m also explain the square root...
Easily learnable video
Perfection
That's cleared that up
The square root is by definition the positive root.
The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side!
can you do a map of philosophy plz
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nice I love this