A-Level Maths: A1-11 Proving √2 is Irrational

[joshuachu]

You sir, are a quality teacher! This video has really helped me grasp the idea of proof by contradiction and now I also understand the proof for why root two is irrational. Better than the numberphiles video! Thank You!

[the-boring-car-guy]

Just blew my mind. Thank you very much

[jackbrasier-creagh]

You absolute legend. This has confused me all afternoon; now ur video unconfuses me in 5 mins.

[javinshah]

man still carrying my a levels 6 years on!

[ht-vefe]

You made this when I was in year 7 and now I am using it in year 12, 5 and a bit years on

[AceOfHearts]

What I dont understand is why it is significant to say it is even... it is the factor of two which is preventing a over b to be a reduced fraction. 'Even' is just a property of having a factor of 2.

[Anonymous-qw]

A good straight forward explanation of Euclid's proof

[nyimalhamo]

Fantastic explanation. This is most similar to the Australian way of teaching. Thank you!

[mfjoyce]

Very helpful video...thank you very much!

[reece]

Thanks a lot really helpful video, I was wondering how the fundamental theorem of arithmetic links to this?

[rahulhdgaming]

Hello Sir - great video . One thing I don't understand is that why the frcation has to be in its very simplest form to show that a number is rational ?

[rohangheewala]

Appreciate these videos so much sir, thank you from the bottom of my heart 👌🏽
I’ve just been pondering over this query since last week because this proof has been making my head spin for a good week now and I would be so grateful if you could put me out of my misery please!
While I deeply understand your teaching WITH the ASSUMPTION that a/b is irreducible, I’m just ever so confused what gives us the mathematical right to rule out the fact that root 2 may be rational just because it contradicts an ASSUMPTION we have made (that a/b is co prime). I’ve been trying to convince myself that a/b is a ratio of each other and so should, or even must be as a ratio in its simplest terms, and therefore a & b must be co-prime... and in fact, I wholeheartedly agree, it only makes sense that a/b is in its simplest form... but what has my head spinning is the thought of root 2 being equivalent to 4/6 (just for example purposes) where A would be 4 and B would be 6. 4/6 can be cancelled down to 2/3 which is rational... While you and I both know that root 2 is NOT rational and certainly not equal to 2/3, but what if root 2 was actually rational, and that a/b was the actual equivalent in fraction form, but just with a scale factor of 2? I am by no means trying to argue or correct you sir, I’m just trying to see where my thinking is wrong and trying to understand why this proof by contradiction proves root 2 is NOT rational? Because from my understanding, the only thing that seems to be contradicted is the idea that a/b IS irreducible despite us saying it shouldn’t be... and so I can’t seem to see or understand how this proof shows root 2 is NOT rational... surely a/b (a fraction) COULD still be equivalent to root 2 but all we have shown in this proof is that a/b just has a factor of 2?
Essentially, what If a/b (A FRACTION) was actually equivalent to root 2, but a/b just so happens to have a factor of 2 which contradicts us ASSUMING a/b is irreducible and so we’ve completely ruled out the fact that a/b may still actually be equivalent to root 2 just because it has a factor of 2 and we just so happened to say it didn’t.
Would it not be better to use a fraction in the form 2k+1/2 or 2/2k+1 (a combination of odd and even numbers) and make that equivalent to root 2 and show through a factorisation or something that no value K would give us root 2? (EDIT: IF THIS METHOD WOULD WORK, HOW WOULD WE OVERCOME THE USE OF 6/9 WHICH IS A COMBINATION OF AN ODD AND EVEN NUMBER, BUT HAS A COMMON FACTOR 3?)
We still contradict the idea that we said root 2 is equal to a fraction and thus we are saying root 2 is rational, but we then go on to show that root 2 cannot be rational, and hence the contradiction.
Apologies for the long winded comment sir

[yasminh]

I have paper 1 tmrw and I am so grateful for this resource thank u so much sir

[ASHISHKUMAR-vmcx]

Thanks you so much Sir ji, "app kaise he" in English means how are you

[Anbu]

Isn't 2k squared k squared plus 4k plus 4?

[Salgandarin]

1:59 What made you decide to square both sides?

[hoyama]

thank you so much that was very helpful☺!!!!

[nosir]

Why does a/b HAVE to be in its simplest form though. Is part of the definition of a rational number a number which can be expressed as a fraction AND in its simplest form? Or is it simply a number which can be expressed as a fraction?

[karotic]

1:20 I’m not sure what you mean here by cancelling the fraction down further than it already is.

in that sense, how would 56/6 be cancelled down further ?

[mikhaelhalbar]

Do you have to prove that a² being even implies a being even??