A Proof That The Square Root of Two Is Irrational

  • Published: 14 October 2018
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    Micorn Stevens
    Edited by
    Hannah Canetti
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    Eric Langlay
    Music by Jake Chudnow and from AudioNetwork
    ***VSAUCE LINKS***
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Comments • 9 439

  • Anthony Arias
    Anthony Arias  3 години тому

    Michel in every video "Or is it?"

    • Simone Cecchin
      Simone Cecchin  7 годин тому

      But id a and b are both even at the end of the video they can be diveded by 2 and for example a is 2 so it becomes 1 and if b is 4 so it becomes 2: now a and b are coprime. Can it make sense? 🙄🤔

      • Poo Poo
        Poo Poo  День тому


        • Sovidquack
          Sovidquack  День тому

          Now we gotta kill you now

          • John Locked
            John Locked  День тому

            16:15 makes no sense. he NEVER proved that a and b cannot be reducible to two co-prime integers. 4 and 6 are both even and they can be reduced to co-prime integers.

            • Rick L
              Rick L  День тому

              He proved that every ratio of integers can be reduced to co-prime integers. So if squareroot of 2 is rational, it should be able to reduced to co-prime integers too which is the ratio numbers only have 1 same factor which is 1. But a^2 = 2 (b^2). Means a^2 = even number, so a is also an even number. If so, then a = 2c. Sub a = 2c into a^2 = 2 (b^2). (2c)^2 = 2(b^2) 4c^2 = 2 (b^2) 2c^2 = b^2 So b^2 is an even number since it's equals to 2 times stg. B^2 = even number means b = even number So if squareroot of 2 is rational, it is gonna be equals to even/even? Which impossible because even/even will always end up giving u a co-prime integer like 4/1 2/3 (all have same factor of 1 only) so this proved that statement "squareroot of 2 is rational" is false. I think you got the wrong point of the video

              • Rick L
                Rick L  День тому

                Wow incredible! How old are you btw? Just wanna know :)

                • wolverine96
                  wolverine96  2 дні тому


                  • DinosaurWithAnAxe
                    DinosaurWithAnAxe  3 дні тому

                    When he wrote the decimal number 0.8 and said YIKES i felt that

                    • Koongtee Chintanakarn
                      Koongtee Chintanakarn  3 дні тому

                      Sqare root -1=1?

                      • Kenny Arias
                        Kenny Arias  6 днів тому

                        Y I K E S

                        • Danny Dazzler
                          Danny Dazzler  8 днів тому

                          What's the square route of 3.6 My math not great not terrible Read more No, literally I mean i should just read more.

                          • Alex Baldwin
                            Alex Baldwin  9 днів тому

                            Micheal: Do you know what an even and an odd number are? Me: I do! Micheal: ...or do you? Me: 😦😦😦

                            • Richard Britton
                              Richard Britton  11 днів тому

                              That’s irrational thinking, if we can make an object 1x1x2and the theorem doesn’t apply, then theorem is wrong

                              • Richard Britton
                                Richard Britton  11 днів тому

                                We can measure the square root of 2, so our math is wrong in some way

                                • Rachel Bazilian
                                  Rachel Bazilian  11 днів тому

                                  I was like half asleep for the very end and he's said "and as always" and I wanted to say "stay awesome, possums👍😉"

                                  • My NewPhone
                                    My NewPhone  12 днів тому

                                    No defintions no answers. All definitions are arbitory so if there are any answers they are all arbitory. All of creation can be defined in anyway the definer defines it. We all live in our own worlds.

                                    • Jay
                                      Jay  14 днів тому

                                      I just finished trigonometry so I have lost the ability to care whether a number is rational or not

                                      • hanstツ
                                        hanstツ  15 днів тому

                                        Love to see HowToBasic teaching math now

                                        • link boy
                                          link boy  15 днів тому

                                          WhAt Is MaTh

                                          • Triodymium
                                            Triodymium  17 днів тому

                                            Oh, my goodness gracious. Look at that. Look at that!

                                            • Edgar Rivera
                                              Edgar Rivera  18 днів тому

                                              This is one of my favorite VSauce videos. I would have loved to have Michael as my math teacher.

                                              • Kenichi Mori
                                                Kenichi Mori  18 днів тому

                                                Roma-ji ローマ字 三三三 = √2×π 三和ゴッドです。

                                                • Kenichi Mori
                                                  Kenichi Mori  18 днів тому

                                                  Directory archive structure square root two conphasitive.

                                                  • Raghav Dhiman
                                                    Raghav Dhiman  19 днів тому

                                                    It just takes a minute to prove it by contradiction method

                                                    • Matthew Beggerly
                                                      Matthew Beggerly  20 днів тому


                                                      • eromana
                                                        eromana  20 днів тому

                                                        PLS use a marker pen !! thin pencil lines are completely illegible on my laptop screen regardless of brightnes

                                                        • Archie Collinson
                                                          Archie Collinson  21 день тому

                                                          Wtf thats so cool

                                                          • OrenWD
                                                            OrenWD  21 день тому

                                                            0:06 and 11:45 michael says that numbers look pretty dude are you like sexually attracted to numbers UMMMM

                                                            • Undergod 666
                                                              Undergod 666  22 дні тому

                                                              Lol i struggled a little with the fraction part so i looked at it and thought about it for a bit, then i saw it, but with my own trick, i just did 1/2×1/2=1/4 because thats easy, and really obvious, and then i looked at it and thought "wait... 1×1=1 and 2×2=4.." and then it clicked.. i feel dumb and smart at the same time.. btw my school never thought me this as far as i know.. or i just didnt pay attention

                                                              • Domasin Kujur
                                                                Domasin Kujur  22 дні тому

                                                                IT WENT OVER MY HEAD

                                                                • Nightdog 12
                                                                  Nightdog 12  23 дні тому

                                                                  Nobody: Vsauce making you question your 4th grade education: 2^2 is not irrational........... O R I S I T

                                                                  • Teresa Night
                                                                    Teresa Night  24 дні тому

                                                                    Makes me miss high school maths.....

                                                                    • Munching Mozzarella
                                                                      Munching Mozzarella  24 дні тому

                                                                      1.414213562374 times 1.414213562374 = 2 *say sike right now*

                                                                      • Mariano
                                                                        Mariano  21 день тому

                                                                        i got 2.000000000002559588516

                                                                        • JuzzTheFuzz
                                                                          JuzzTheFuzz  24 дні тому

                                                                          Sir, sir... just take your change and leave

                                                                          • Carson Archibald
                                                                            Carson Archibald  25 днів тому


                                                                            • Shane Napolitano
                                                                              Shane Napolitano  27 днів тому

                                                                              He draws his 8’s like that

                                                                              • Zach Bills
                                                                                Zach Bills  27 днів тому

                                                                                You could have stipulated a and b were coprime when you defined them and immediately had the contradiction without having to iterate the argument.

                                                                                • Not the Real Tfue
                                                                                  Not the Real Tfue  27 днів тому

                                                                                  *2b or not 2b?*

                                                                                  • Matthew Thorpe
                                                                                    Matthew Thorpe  28 днів тому

                                                                                    This is great, but can Micheal's brain run Crysis? Is it that amazing?

                                                                                    • GoatzAreEpic Maokai
                                                                                      GoatzAreEpic Maokai  29 днів тому

                                                                                      learning all the math so i can study cs in 1.5 years

                                                                                      • Riel de bonk
                                                                                        Riel de bonk  29 днів тому

                                                                                        I guess you could call it Integerational

                                                                                        • The Technician
                                                                                          The Technician  Місяць тому

                                                                                          One issue: At 2:22, Michael states that a fraction that ends makes it rational (aka if sqrt 2 actually ends then it is rational). This is not true, as a number like 1/3 is rational but is never ending.

                                                                                          • Eyal Kalderon
                                                                                            Eyal Kalderon  28 днів тому

                                                                                            Well, he's technically not wrong. If your expansion ends, it _must_ be a rational number. Sure, some rational numbers exist that do not have this property (like 1/3 and 2/3), but there are no irrational numbers whose decimal expansion ends. Still, I agree with what you're saying, and I wish that Michael had clarified that having a finite decimal expansion is not a requirement for being a rational number, but technically he still didn't say anything false.

                                                                                            • Irfan Ahmad
                                                                                              Irfan Ahmad  Місяць тому

                                                                                              Watch and comment Which one is true? uaclips.com/video/sbGjr_awePE/відео.html

                                                                                              • mr.origami
                                                                                                mr.origami  Місяць тому

                                                                                                square root of 2 is not rational number but how are we sure that it is irrational number?

                                                                                                • Mariano
                                                                                                  Mariano  Місяць тому

                                                                                                  Because irrational numbers are defined as real numbers that are not rational

                                                                                                  • Jonathan Bartles
                                                                                                    Jonathan Bartles  Місяць тому

                                                                                                    Integers are rational but your saying "either" implies integers can't be rational

                                                                                                    • 64 Bit Music inc
                                                                                                      64 Bit Music inc  Місяць тому

                                                                                                      *cries in JEE*

                                                                                                      • Ekaterina valova
                                                                                                        Ekaterina valova  Місяць тому

                                                                                                        At 6:28 - is that how americans do binomial multiplication cause in my country we had a formula (a+b). (a+b) = a^2 +2ab +b^2

                                                                                                        • Chocoberry Brownhouse III
                                                                                                          Chocoberry Brownhouse III  Місяць тому

                                                                                                          americans have that too but the general version of binomial multiplication is used when your formula can't be. (a+b) * (c+d) = ac + ad + bc + bd

                                                                                                          • WET POTATO
                                                                                                            WET POTATO  Місяць тому

                                                                                                            Michael: Yikes! The entire universe: AAAAAAAAAAAAAA

                                                                                                            • Vertex 12
                                                                                                              Vertex 12  Місяць тому

                                                                                                              Bothers me how he writes the number 8

                                                                                                              • Lastrevio
                                                                                                                Lastrevio  Місяць тому


                                                                                                                • Worrien Battlefield
                                                                                                                  Worrien Battlefield  Місяць тому

                                                                                                                  But then the root of 4 is irrational too if you change the 2c into 4c

                                                                                                                  • Mariano
                                                                                                                    Mariano  Місяць тому

                                                                                                                    If you try to prove root 4 is irrational in the same way, you will find a problem in the part where we say "a^2 is even, so a is even". You would need to say "a^2 is a multiple of 4, therefore a is a multiple of 4", but that is simply not true (for example, 4 is a multiple of 4 but 2 isn't).

                                                                                                                    • Haider Salam
                                                                                                                      Haider Salam  Місяць тому

                                                                                                                      I just have a question about a part of the proof that confused me (I only did math until IGCSE so thats why i am asking lol) but what justifies the part where Vsauce says that because B2 is even then B is even because the rule he said if i Understood is that if you take an even number and square it then the result is even. but he didnt say that if he takes an even number and square root it then it is also even. I mean shouldn't that be another rule that needs to be assumed for the proof to be true or does it logically follow from saying that if you square an even number then it is even then that also means if you square root an even number then it is also even. Can someone clarify that for me please?

                                                                                                                      • Haider Salam
                                                                                                                        Haider Salam  5 днів тому

                                                                                                                        @MuffinsAPlenty I see! yeah that makes sense thank you. I mean obviously i didnt think the proof is wrong I just didnt see where he justified that move but yeah it makes sense now :)

                                                                                                                        • MuffinsAPlenty
                                                                                                                          MuffinsAPlenty  5 днів тому

                                                                                                                          His justification there wasn't correct, but the fact itself is correct. The two facts you need is that every integer is either even or odd, and that the square of an odd number is odd. At the beginning of the proof, we stated that "a" is an integer. So we know that a is either even or odd. If a were odd, then a^2 would be odd; however, we know a^2 is even, so it follows that a could not be odd. Since a is either even or odd, but a is not odd, it follows that a must be even.

                                                                                                                          • achpek13
                                                                                                                            achpek13  Місяць тому


                                                                                                                            • Mohit Bling
                                                                                                                              Mohit Bling  Місяць тому

                                                                                                                              Any indian who thought of the proof of this taught to us in class 9th and 10th

                                                                                                                              • Miyuki Teishi みゆちゃん
                                                                                                                                Miyuki Teishi みゆちゃん  Місяць тому

                                                                                                                                But what about a number like *0.8* Y I K E S *dissolves into nothingness*

                                                                                                                                • Gerben van den Berg
                                                                                                                                  Gerben van den Berg  Місяць тому

                                                                                                                                  I learnt this in class.

                                                                                                                                  • Max Andersen
                                                                                                                                    Max Andersen  Місяць тому

                                                                                                                                    "Dude, that was awesome"

                                                                                                                                    • Sergiu Andrei Sabou
                                                                                                                                      Sergiu Andrei Sabou  Місяць тому

                                                                                                                                      I guess very few take into consideration the possibility that our mathematical language is too primitive to be used for representing the truth about this universe we live in.Maybe the very concept of number is a wrong way to start the journey to allknowledge.Maybe we should invent another math language from scratch.

                                                                                                                                      • ComedyCenter
                                                                                                                                        ComedyCenter  Місяць тому

                                                                                                                                        My biggest issue is the way that you write 8

                                                                                                                                        • Oddy Andy
                                                                                                                                          Oddy Andy  Місяць тому


                                                                                                                                          • proud man
                                                                                                                                            proud man  Місяць тому

                                                                                                                                            Thanks for explaining

                                                                                                                                            • Harshal Tholambia
                                                                                                                                              Harshal Tholambia  Місяць тому

                                                                                                                                              Most of part was the summary of my maths ch.1 Edit: though it was a revision for me ..

                                                                                                                                              • d0
                                                                                                                                                d0  Місяць тому


                                                                                                                                                • ExoAssassin
                                                                                                                                                  ExoAssassin  Місяць тому

                                                                                                                                                  Wait why is the thing for a odd number not 4(c^2+c)+1 it’s 2(2c^2+2c)+1?

                                                                                                                                                  • ExoAssassin
                                                                                                                                                    ExoAssassin  Місяць тому

                                                                                                                                                    Mariano aah thank that makes sense I just just always told to simply everything so that’s why I got confused

                                                                                                                                                    • Mariano
                                                                                                                                                      Mariano  Місяць тому

                                                                                                                                                      Because we want to write the expression in the form 2n+1, not 4n+1 Both expressions are true, but the second one shows the information that we care about for this proof

                                                                                                                                                      • pinkman punk
                                                                                                                                                        pinkman punk  Місяць тому

                                                                                                                                                        *who writes the number 8 as two seperate circles?*

                                                                                                                                                        • Bob West
                                                                                                                                                          Bob West  Місяць тому

                                                                                                                                                          So, Michael... Is "odd" and "even" just an abstract concept, or does it correspond to anything in nature?

                                                                                                                                                          • Jayden Hashbrown
                                                                                                                                                            Jayden Hashbrown  Місяць тому

                                                                                                                                                            -13 is 2x(-6)+1 not 2x(-7)+1

                                                                                                                                                            • Jayden Hashbrown
                                                                                                                                                              Jayden Hashbrown  Місяць тому

                                                                                                                                                              Nvrmd I messed up

                                                                                                                                                              • Олег Блохин
                                                                                                                                                                Олег Блохин  Місяць тому

                                                                                                                                                                It is not about our Universe, just about math we used to think as only possible one.

                                                                                                                                                                • سعيد سليمان
                                                                                                                                                                  سعيد سليمان  Місяць тому


                                                                                                                                                                  • VSEPR T
                                                                                                                                                                    VSEPR T  Місяць тому

                                                                                                                                                                    @14:06 you are supposing that b is finite number. Otherwise you cannot bring to otherside. Inf=inf 2*inf=3*inf Cancel infinity from both side. 2=3.

                                                                                                                                                                    • Theo Beresford
                                                                                                                                                                      Theo Beresford  Місяць тому

                                                                                                                                                                      That’s the whole point of the proof. You assume that a, b are finite integers which are coprime and show that the assumption is incorrect.

                                                                                                                                                                      • Tacos W
                                                                                                                                                                        Tacos W  Місяць тому

                                                                                                                                                                        Too much maths

                                                                                                                                                                        • Olivia Robinson
                                                                                                                                                                          Olivia Robinson  Місяць тому

                                                                                                                                                                          Bro the square root of two is -2

                                                                                                                                                                          • MikeRosoftJH
                                                                                                                                                                            MikeRosoftJH  Місяць тому

                                                                                                                                                                            Since when is (-2)*(-2) equal to 2?

                                                                                                                                                                            • fangere
                                                                                                                                                                              fangere  Місяць тому

                                                                                                                                                                              Wouldn't that proof for squares being odd or even be dependent on c being an integer?

                                                                                                                                                                              • Theo Beresford
                                                                                                                                                                                Theo Beresford  Місяць тому

                                                                                                                                                                                If a is an integer, which it is assumed to be so, then a^2 must also be an integer so c must be an integer if a^2 is even.

                                                                                                                                                                                • Kayan Dt
                                                                                                                                                                                  Kayan Dt  Місяць тому

                                                                                                                                                                                  The best high school mathematics teacher I never had

                                                                                                                                                                                  • SHAZZAD RAHIM
                                                                                                                                                                                    SHAZZAD RAHIM  Місяць тому

                                                                                                                                                                                    In Bangladesh, this proof is taught at standard 9.

                                                                                                                                                                                    • Hack Codex#⃣
                                                                                                                                                                                      Hack Codex#⃣  Місяць тому

                                                                                                                                                                                      Can someone explain to me why 1/3 is rational?

                                                                                                                                                                                      • Silver - gaming n more
                                                                                                                                                                                        Silver - gaming n more  Місяць тому

                                                                                                                                                                                        You can write 1/3 as 1/3 irrational numbers don't let you do that