Proof - The Square Root of 2 is Irrational

[Cadabena]

@chopchop190 it has to be in lowest terms so that the common factor point of 2 down later on has meaning and relevance. Think of it as a "we'll come back to this later", then when (spoilers! ;) ) p & q turn out to be even, they can use the lowest terms statement as a contradiction. Hope I've not confused you further :)

[chopchop190]

why does p/q has to be in the lowest term? someone explain pls!!!!!!!!

[TheDBZisepic]

I understood what he did, but I don't see how the two numbers being even proves anything. Let's assume we don't know what the square root of 2 is. And say... p is 4 and q is 6. Yes, they're both even but it simplifies to 2/3, which is thus simplified and in lowest terms. So, nothing is proven in my eyes.

[irmb5teS]

@TheDBZisepic yea but since both numbers are even, it means they can be simplified, but we stated that they are already simplified b4, at the start, they shouldn't have any common factor.

[darktaile]

just so we stop arguing about 5th grade math, the square root of 2 is irrational, as the video explains. 2 squared is 2 X 2. 2 squared however, is 4. another example: square root of 4=2, 4 squared =16

[mahaman55]

I wish my handwriting was this good xD

[mahaman55]

I feel smart understanding this ^.^

[natascha97]

OMFG he's so hot!

[YoGotPwndV1]

@LogicalStochasticism but sqrt(4) is irrational...

[automaticSOM]

@YoGotPwndV1

No, it isn't.

[YoGotPwndV1]

@automaticSOM yes it is

[automaticSOM]

@YoGotPwndV1

Are you saying that 2 is irrational?

[YoGotPwndV1]

@automaticSOM no, im saying sqrt(4) is irrational, god read the comment, you blind or something?

[automaticSOM]

@YoGotPwndV1

Yes but sqrt(4) is 2.

[YoGotPwndV1]

@automaticSOM no it isnt, jesus how dumb are some people?

[automaticSOM]

@YoGotPwndV1

Yes it is, put it in to your calculator.

[YoGotPwndV1]

@automaticSOM exactly, my calculator says sqrt(4) = sqrt(4)

i think theres a problem with your calculator

[automaticSOM]

@YoGotPwndV1

2 squared = 2*2 = 4. Therefore sqrt(4) = 2. If you dont know that, you dont know anything.

[YoGotPwndV1]

@automaticSOM no, 2 squared = infinite

anything squared is = infinite

god, what do they teach in modern schools?

[limetang]

@YoGotPwndV1 Are you a moron? 2 squared is not infinite. 2 squared is by definition 2 x 2. That is to say it is 2 lots of the number 2. That is to say it is 2 + 2. That is to say it is 4.

[YoGotPwndV1]

@limetang wow, people are such idiots these days, go back to school and learn maths

[limetang]

@YoGotPwndV1 I'm not the one who needs to go to school and learn maths.

[YoGotPwndV1]

@limetang you are if you think its possible to find 2 squared

[limetang]

@YoGotPwndV1 Two squared is 2 x 2. Are you saying that no solution exists for 2 x 2?

[YoGotPwndV1]

@limetang dont be ridiculous, two squared is not 2x2, 2x2 is obviously 4

as you can see, a solution exists for 2x2, but not 2 squared

[limetang]

@YoGotPwndV1 If you square a number you multiply it by itself. 2 squared is 2 x 2. This is true by definition you fucktard.

[YoGotPwndV1]

@limetang ...wow, im just not gonna talk to such idiots anymore

[limetang]

@YoGotPwndV1 Anyway. It's been fun playing with you troll. Although if you aren't a troll... wow 'nough said.

[Cai278]

@YoGotPwndV1 your dumb

[YoGotPwndV1]

@Cai278 know ur dum

[Cai278]

@YoGotPwndV1 you don't even know how to spell dumb

[YoGotPwndV1]

@Cai278 yeh i no how 2 spel ur jus an idoit so u cnt understande

[lebagelboy]

this just blew my mind!

[okzoia]

Taking the square root of a positive natural number will also yield a negative number as one of the roots. Does this need to be "factored" in also when doing the proof?

[automaticSOM]

@okzoia

By convention the square root of a number is always taken to be the positive root. eg. root(4) = 2 not (-2).

[619brian619]

@automaticSOM no, square roots are positive and negative sqrt of 4 is 2 or - 2

2*2=4 -2*-2= 2

[automaticSOM]

@619brian619

I just meant that 2 is taken to be the principle square root of 4. It is, for instance, what you get if you put sqrt 4 into your calculator. However technically -sqrt4 = -2.

[Dotapoy]

Hello im so dumb in math ! >.< hey sqrt of 25 is 5

[Somaliland009]

it is great video......well done many thanks

[kdepro]

thank you so much. clear, concise, and better than my math professor

[bicnarok]

maybe the square root of 2 is 1, as well as the square root of 1 being 1. Maybe our math is wrong and a number can share a square root. Seems to me people just make things up as they go along by adding letter.

[govnajedemdanas]

@bicnarok You're retarded.What is 1x1?1.That's why the square root of 1 is 1.

Our math is not wrong.It's impossible for it to be wrong as it was made by us.

[quagmire444]

@bicnarok i have to agree with govnajedemdanas. thats probably the most retarded statement ive ever heard lol. youve been taken to many drugs postmodernist hippy.

[CopyCatA]

@bicnarok how old are you?

[TheZarinaStannard]

Thanks, I am 11, and I understood it well, your description and method of teaching is superb and I shall show this video to my tutor.

[lister101]

@TheZarinaStannard Im 11 too. We have our SATs coming up in a couple of weeks.

[TheZarinaStannard]

@lister101 I'm 12 now :P

[lister101]

@TheZarinaStannard I'm twelve in December. I already know some hard equations. Example: Pi x r2 = the area of a circle. But that was just me looking at wikipedia. :) Also, Pi= 3.14159265358979...

It's an inferdecimal. Sorry, im over loading your brain LOL

[YoGotPwndV1]

@lister101 woooow, so complicated... -.-'

[mogstah]

@lister101 using Pi to find the area of a circle is a hard equation? Wow... And you're just conceptualizing this at age 12?

It's not others brains you're overloading, it's your own.

[meiringluke3]

but using this logic, couldn't i prove that all root(25) is irrational? or root(n)? What prevents that?

[anticorncob6]

@meiringluke3 We assume that sqrt(25) = a/b in lowest terms.

a^2/b^2 = 25

(b^2)*25=a^2

Thus a^2 divides by 25, but that doesn't mean a divides by 25. It means a divides by 5, which it does: 5/1.

When we say a^2 divides by 2, we know for sure a divides by 2. That's what falls in your logic.

[KoSa33333]

Oh I mean pieces not peaces :D

[KoSa33333]

Easier to say at the point of 2(q^2)=p^2 that if we decomposed both sides to the factor of prime numbers, on the LHS there would be odd pieces of factors of 2 (at least 1) while on the RHS there would be 0 or even peaces of factors of 2 for sure (both p^2 and q^2 contain 0 or even peaces of factors of 2 because of the square).. That's the contradiction because a number can't have more then one different prime factor decompositions.

[gmussina]

not to steal your thunder, but at my school they would dock points if you didn't prove that if 2 divides p^2 then 2 divides p(contraposition would be easiest); unless it's already clear that has been proven previously.