# A Proof That The Square Root of Two Is Irrational

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joshie oshie14 minutes agoMy fear of gimps is erational.

LosingLukeHour ago“A proof”

LosingLuke2 hours ago**writes 8 as 2 0’s**

Park Justin8 hours agoBecause they will always be even even after factoring out 2. That makes it go on forever.

Veteran Mainiac10 hours agoDraws an 8

*ooooh man*

Draws 0.8

*realeases*

Aisha11 hours agoThe big bubble numbers and clean writing is so soothing to my eyes

wkf111412 hours agoI think you probably need to add more explanations to be more comprehensive. In the first half part, you proved an even number's square is still an even number. However, you didn't prove the reverse case. Which means, the square root of an even number has to be an even number, or integer (such as 2, 6, 8, 10, 12, 14 etc.). Thus, at 14:36, square of "a" is equal to two times square of "b", which is an even number. But, you need some discussions that "a" could be a not-integer or an even number. Both cases violate the assumption of "a" and "b" are coprime integers.

Jimin Is A Living MochiDay agoI don’t understand a word he’s saying but this is fascinating

omarPIMP DADDYDay agoThis is all the math I learned in my life in 17 minutes

Greyson MillerDay ago*Y**i*kE*s*

ZacPlayzGamerDay agoI just learned the Pythagorean Theorem in pre al today XD

CrossdownstreetDay agolol just use a calculator

WiktorRapBattleDay agoYIKES

jgms2 days ago*YAAOZAS*

Andrew PLas2 days agoPLUS OR MINUS the square root of two

GAMING ST2 days ago1 min problem extended to 20 min and I was still enjoying that.😂😂

Superbrains Video Game Lord3 days agoMichael should teach math more often

Elijah G3 days ago^{+10}2:32 he didn't use the true Vsause music this is an imposter

Evan Guzman3 days ago👀

👃🏻

👄

👕

👖

👞

This is Bob.

Bob said hi.

This is Bob when the bus goes by.

XX

👃🏻

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👞

Jye-Ming Serres3 days agoyiikkkesss

βΣΨΩΠD RΣΔSΩΠ3 days ago^{+1}Be my math teacher.

Gerrit Schimmelpenninkc Mosse3 days agoDude makes maths interesting

Fancy in the House3 days ago4:30

-12+1 is -11 not -13

MarianoDay agoYes but 7*-2 is-14 not -12

qimaru3 days agoa proof?

Pyrosmantia3 days ago-12+1=/=-13

MarianoDay agoWhy -12 tho, 2*-7 is -14

Bijoy Lakshmi4 days agoThanks

Mi 284 days ago^{+11}Dong status: fully expanded.

Konstantinos Koufakis4 days agoThe maths in this video are literally primary school stuff

hey73282 days agomost people don't even know primary school maths

IamSaki4 days ago*YAAWZAAA*

Dalton Freeman4 days agoplease tell me there's a "Yeowzahs!" gif somewhere

unlucky7rusty boy4 days agoWait is every fraction technically one if you simplify it enough.

Christine Gago4 days agoWait what? I lost you at 0:00

Cabecool10 / Skelemaster7674 days ago^{+2}*Y O W Z A S*

dom cusano4 days agoI like how perfectly he draws his 8s

yoyoman5 days ago7:16 😂😂yausaaaa look at this results😂😂

Rjfh ubfofhfuxifohfhfhfjfjghdih. Kxgcj jckfb jpcocjoccoh jvhxk np n nlvncochovjco b nckcn oj hlccgcpnvnlconvnlcohcjfbfohvnovhclhch jp lhfocj j jokfgfoh ojvjlcoh jdldjcpjdhfpjvj j k

Sorry.

JOY IN RANDOM5 days ago^{+9}How long did you spend trying to find a loop hole

Arpit Soni5 days ago^{+1}I am an Indian and I already studied it in my 10 standard

mychemicaljulia5 days agowhy did i take functions

foil5 days agooh hey, apparently im a math term now aha

Dv3v5 days agoi wish you were my math teacher

Bladed Sinicle5 days agoDink donk

Fire Oblivious5 days ago^{+2}Why is his room so dark?

Not Gay4 days agoOblivious 606 lighting

MontyTheGod5 days ago“Yikes”

Kaan Soytaşoğlu5 days ago17 minutes of nothing

MMGeri5 days agothis is actually recquired for graduation in my country

Sophia Ziegler5 days ago4:51 *-6*

fulcrum 295 days agoI am more confused more than ever

V E K T O R5 days agoDy Michael!!

I drew 8 in my childhood just like you!!!

IB5 days agoWe can prove that √2 is irrational by assuming that √2 is rational and and √2 = a/b where , a and b are +ve integer and co-prime number easy pisy 😋

Cory Baxter6 days agowho's Micorn Stevens?

Cory Baxter6 days ago1.41421356237 x 1.41421356237 = 2

Dude Mc Broham6 days agoIve never been so invested in proofs before as i was just now

JoãoZinhoCraft #BRENOPOLIS1MILHÃO6 days agoisn't this proof supposed to be simple

Trying2 Understand6 days agoI would love to see the proof of :

p/(p-1) = 1/p^0 + 1/p^1 + 1/p^2 + 1/p^3... for all p>1

Alterate6 days agoliterally my intro to discrete math class

ranimations6 days ago^{+1}I just adore how you, when you were ubderlining even and odd multiplications at just before 17:21 you underlined the even part twice (even) and the odd once(odd)

Shae Perkins6 days agoHey, DONG! Michael here.

Arhum Mudassir6 days agoI had a good understanding of math but now I have a lot of questions about the universe

Noel Crist6 days ago^{+1}If you divide 2 by 2 which are both even then it leads to a odd 1.

*MEEPO* the mushroom dealer6 days agoThanks Einstein

UY Scuti6 days agoIts not hard to believe

MeTheGuy 126 days ago^{+2}Michael was losing an argument so he made this video

Kızıl Link6 days ago0.12 two of them is 4 lmao

nithin raaja7 days agowhy can't he use the identity (a+b)^2=a^2+2ab+b^2

DREAMER SINCE 19XX7 days agoif 2c+1 is odd...then what about 2c-1

TweedierCastle6 days ago+DREAMER SINCE 19XX should he mention 2c-3 and 2c-5 are odd too?

TweedierCastle6 days agoOdd too lmao

Blake McConnell7 days ago1 is an “awd” number -Michael

TotallyHorsed7 days ago^{+3}you can't discover anything in mathematics without looking "at the universe itself".

Your brain exists in the universe already, so by extension the thoughts within the brain are within the universe. This is the universe discovering itself through your brain.

hey73282 days agoaaand you missed the point.

TheGamingOstrich7 days agoI should be in bed rn

Bob The Boss Saget7 days agoKickin it w vsause doin up them algebraic proofs like some savages.

Alec Ray7 days agoI learned more in this video than I ever did in Algebra of Calculus

Reid LeBlanc7 days agooh boy binomial multplication

Glumbor Tango7 days agoy o w z a !

I want die7 days ago11:22

Fudmottin7 days ago^{+7}√2 was known to be irrational prior to algebra. So there should be a geometric proof. Can you construct one?

Cyberplayer54 days agothexvid.com/video/yk6wbvNPZW0/video.html I think this video show how to do that.

I want die7 days agoI watched it, you happy yet youtube?

Peter Griffin7 days ago^{+6}This did not help me for my tomorrow's maths exam

TheSmartyPants7 days ago1st chapter grade 9 ncert CBSE India 🤦♂

Brad8 days agoI thought this was going to be some new proof, but nope. Just the same proof used for thousands of years.

Jerakk308 days agoMy favorite number is 27. Why is 27 my favorite number? Because of some beautiful proofs about it. 27 is the cube root of 19683. The sum of the digits in 19683 equals 27. Both numbers are divisible by 9 which, without dividing, can be proven because the final sum of all numbers in both sets equals 9. Any number number multiplied by 9 has an answer where the final sum of that answer is always 9.

Jeff Sandt8 days ago^{+12}That was a strange effect when he says yikes at 0:13

Ger -3 days agoIt’s like the rolling shutter in the distortions video he made

thexvid.com/video/mQ0hS7l9ckY/video.html

Death Gaming8 days ago^{+2}I had to prove this for my Discrete Maths class

Pretty Ricky8 days agoDeath Gaming same

Ailesh Amatya8 days ago^{+3}why do i feel like this is like Vsauce

Nick Falk8 days agoTHOSE AREN'T EIGHTS THEY'RE SNOWMEN! STOP IT!!

Igor Matias8 days agoThis gave me goosebumps.

Ádám Győrfi8 days agoLove the way of explaination;)

Juliane Lust8 days ago^{+1}Why should the square root of 2 be rational?

I want die7 days agoThis video just proves it, because like he says, we can't assume.

lil volu8 days agoYIKES

James Cabrera9 days agoDISCREET MATH

David Cely9 days agoI think the title is wrong. He proved that square root of two is not rational. To proof that it is irrational is harder, it has something to do with the least-upper-bound axiom. See Apostol Calculus 2ed (section I3.13)

Paul 1230988 days agoNope, it's a valid proof. If we talk about only the Reals as the metric space, proving square root of two is not rational proves that it is in fact irrational .

Edits JAG9 days ago^{+6}I learned this on sophomore year of high school when reading principles of mathematical analysis by walter rudin, I wish that I could have seen this video instead of reading the proof, which was very confusing

zoiyoknd9 days agoDong, but if you apply same to sqr(4) it may seem it is irrational. I think you need first to proof sqr(2) is less than 2 and greater than 1.

Mariano8 days agoNot really, you can apply the same line of reasoning to sqrt(4) and you will never reach a contradiction

thesnusmumric9 days agoOh come on! if A is even then A^2 is even - was prove. But if A^2 is even then A is even - actually was not prove, but was used

möhre möhre9 days ago^{+1}Anyone Else noticed how he write an 8?😂

Adam Hunt9 days agoQuite a fun proof, did it in maths

Ahmad Kashmar10 days agoSeriously, why don't you go and prove it yourself instead of watch this?

Vincent Li10 days agoBut even numbers like 2 can be expressed as 2/1(And because 2 is definitely rational), so when a/b=c and c is even, you can express it as c/1. I mean, you don’t have to go on forever, if you take the actual answer of the square root of 2, it is possible to express it as a fraction, therefore it is rational.

Vincent Li8 days agoMariano Oh... oops

My bad

Mariano8 days ago+Vincent Li He never said anything even close to "the square root of 2 is even", you must have heavily missunderstood some part of the video

Vincent Li8 days agoJodie Waits I’m talking about the square root of 2 here, which according to Michael is even. In fact, natural numbers, integers, and fractions are all rational. So if the square root of 2 is even, the fraction is simply n/1. That’s rational.

Jodie Waits9 days agoAlso, even/odd are concepts that only apply to integers. You'd have to prove that a/b reduces to an integer before you can call a/b = c is either even or odd to begin with.

Jodie Waits9 days agoFor instance, 2/2 = 1.

Pablo Longoria10 days agoWatching this video gave me flashbacks to middle school, when my teacher used to get mad with me on tutoring because I didn’t understood anything of what she was saying.

Gentle Path10 days ago^{+1}YAUZAS!

Gawain_Goat10 days agoI am now going to use this as a warm up before math tests.

corcorwhite10 days agoBro I cannot get over how you write your 8s lol

PatDoesThings - Games10 days agoMay I ask, who tf cares