A-Level Maths: A1-12 Proving √3 is Irrational

[zhangyun]

Why are people calling you Paul😂? You videos are very good though.

[snp]

Hi Paul, would this come up in the exams?

[tomatomath]

Hi, is this playlist also relevant for cambridge further math?

[jeff_kola]

How would you prove that an even number is irrational through contradiction like root 6? Since the numbers that could multiply to give the final outcome varies.

[MarwanNazif]

Hi Paul, I was just wondering how do we know A/B is actually in it's simplest form?

[veem]

Regarding your explanation of.... "if a^2 is a multiple of 3, then a is a multiple of acknowledged! However, could you please sanity check the following and see if it meets your approval. As we are discussing Proof by Contradiction then why not use it to prove if a^2 is a multiple of 3, then a is a multiple of 3? Hence...

Assume: a^2 is a multiple of 3, then a is NOT a multiple of 3.

If a^2 is a multiple of 3 then a^2 = (3n)^2 where n = a positive or negative integer.

Therefore, a^2 = 9n^2

Consequently, a = SQRT(9n^2) = 3n (which is a multiple of 3 and therefore a contradiction of the Assumption).

Assumption is invalid, therefore, if a^2 is a multiple of 3, then a is a multiple of 3.

Is the above a valid argument?

[anish]

What about proving root 6 is irrational, you said it would work for 5 & 7 but would it not work for 6?

[dbw]

Hi Jack, is that by any chance a princess mononoke shirt?

[taqiya.b]

Surely if a^2 has a factor of 3 it doesnt necessarily mean that a is a factor of so shouldnt the one side arrow be the opposite way round as the reverse is always true?

[mathstutor]

Which root 3 is irrational proof do you suggest we do in the exam?

[scot]

I understand why "a^2 = 3b^2" means that "a^2" is divisible by 3, but I am still confused and unclear on how that means that "a" must also be divisible by 3

[Stev]

Hi,
doesn't this proof fail in that it maintains that the square root of 4 cannot be rational but in actual fact this is the case??