Proof that Square Root 2 is Irrational

This video is housed in our WCoM Basics: College Algebra playlist, but it's important for all mathematicians to learn.

Tori proves using contradiction that the square root of 2 is irrational.

[frepi]

I love black boards. Lately, I attended classes where the teacher used a computer screen projection and this was so bad for learning. Black boards force the teacher to teach at the same pace that he or she writes. It allows the students to take notes and ask questions.

[GurshaanGaming]

I was not able to sleep so that’s why I am watching this vedio

🤭🤭🤭🤭😴
But now I am going to sleep

[amitgupta-sixw]

Excellent explanation i understood more than any other video I watched

[omargoodman]

To all the people criticizing the assumption of an irreducible fraction, it's a non-issue because the canonical form of a fraction is equal to any multiple thereof. So, even if we assumed that sqrt(2) is equal to some fraction, c/d, that isn't in lowest terms, c/d can be reduced to a/b anyway. Therefore, sqrt(2) is still equal to a/b where a and b share no common factors.
This is basic part of the definition of a *rational number* that originated in ancient Greece during the time of Pythagoras in around 6 BCE. The "Pythagorean Order" believed that all numbers were perfect and divine and that any number could be expressed as a ratio two integers. Even an infinitely repeating decimal like 0.333... can be expressed as 1/3. If you couldn't calculate it down to a perfect ratio of just two integers, you just hadn't calculated enough. It was this very proof of sqrt(2) that demonstrated that there were, indeed, numbers that didn't follow this perfect structure; numbers that were irrational (cannot be expressed as a ratio of integers). And later, still, it was found that you can even go a step further. Even for irrational numbers like sqrt(2), they found that you could still describe them using an algebraic formula, using algebraic operations; exponents, addition, subtraction, multiplication, and division. These are now called Algebraic Irrational Numbers. But there are some that don't even obey that paradigm. Transcendental Irrational Numbers like _e_ and _pi_ won't even take an algebraic formula; the formula would keep going on and on with an infinite number of terms.

[roninwarriorx]

I design the majority of my artwork in a root 2 rectangle. Phi is my favorite but 2 is easy.

[tejbahadur]

this just cant be true,
so you are telling me that this is for college students ?
i am an indian, 14 year old and this is in my first chapter of maths book

[niceguy]

What about if this logic applied in a rational number? Will it be true?

[wanwisawonguparat]

I don't understand something in your proof.
Why a and b haven't common factors?
(I'm not good at English . Sorry about it.)

[donynam]

Let's use this method to prove that Square Root 3 is Irrational number.

[rmnalpha]

I enjoy her voice you also enjoy it 😂😂
👇 Like whose enjoy her voice

[himanabhdixit]

Hello madam
You teach very well
Love from India

[abdulhadi_abbasi]

Greatly explained mam .You highlighted each and every important point .Thank you very much .Your video widely helped me

[silverruv]

It will come in board exam 100% garentee

[rajendranchockalingam]

Good morning madam
Super explanation and very simple way to understand
I am from Tamil Nadu.
Thanks

[MamtaKumari-ctkj]

Really it's so helpful....I can't expected that even I will understood your language or not but my expectation was wrong....😁 really it's so nice c video I have understood very well👍🏻 thnx so much

[samarjeetpal]

It was a very helpful video..I've been looking for explanations for this theorem, but I didn't understand any of them...thank u so much..

[gsssmustfapursurajsingh]

EXCELLENT MATH TEACHER PRAISE WORTHY WORK

[ramya]

Very super mam your a good teacher of youtube and all videos super explanation is very good and this video is very useful of irrartion numbers thank u mam bye...

[idontknow-msmc]

Great explanation! I was watching a lecture for another class and the instructor mentioned this as an example of proving by contradiction and he definitely didn't spend 6 minutes talking it out, so much appreciated. I just subscribed, haha.

[MrFeatre]

If I had a teacher like her, I would go for Math classes everyday..