You go wrong at 3:58 because a/b being rational does _not_ imply that a and b have no common factor, for example 14/21 is still rational, but the fraction is merely not in its lowest terms. You already have enough at that point to finish the proof. You found that both a and b have a factor of 7, and that _in itself_ contradicts the assumption you made at 1:38 meaning that one of your initial assumptions is false, and we can always put a fraction in its lowest terms, so the only assumption that could be false is the rationality. That means that √7 is irrational. Let's be clear, the definition of a rational number is one which can be expressed as the quotient of two integers. An irrational number is defined as one which is not rational. In brief, the two initial assumptions are : (1) that √7 = a/b where a, b ∈ℕ, and (2) that gcd(a, b) = 1. That leads to a contradiction of (2), which then proves (1) is false, i.e. the assumption of rationality is false.

Assume a/b =√7 --> a = b√7 --> a^2 = b^2 * 7 We're going to now do the prime number factorization of the left side and the right side. If both sides are equal, then their prime number factorizations must also be equal. p1 p1 p2 p2 p3 p3...pn pn = q1 q1 q2 q2 q3 q3...qn qn 7 Every prime factor of "a" must appear twice in the factorization of a^2. Same for "b" and b^2. But, on the right side, we have one unpaired prime (7)! That singleton 7 proves that the prime factorizations on the left and right of the "=" sign cannot be the same. Why?... the factor 7 must appear an EVEN # times (0, 2, 4...) on the left, and an ODD # of times (1, 3, 5...) on the right side. The assumption we adopted cannot be true.

this was a cool explaination! im currently in grade 12 functions, is this the type of content I will be covering at universtiy level? Would you say this is one of the harder things to grasp for a student out of highschool? Also, what kind of 'excersices' could I do to try to help build up application??

How do you solve this same equation without the value of n?

So incredibly helpful!! Thank you so much

2025 attendence like this comment

Thank you sir

Where did you get that 9 in the middle

Thank you Sir,this is really helpful

2025 attendance

heyy , thanks

My brother you are the GOAT

Here cuz of an exam thanks I get it now

What a wonderful and easy method 🎉❤

Bro realy I loved your teaching continue on it😘😍

Im so gonna ace this math test😂❤

cleared my simple doubts thank you very much

Your educational content is so well-organized and informative! You really make complex topics easy to understand. Have you ever thought about creating interactive lessons or quizzes for your audience?

gREAT GUIDE

Nice Sir ❤

Please Sir help us solve alpha cube minus beta cube

thank you 🤍

i got 114 determinant im not sure where i went wrong or where proffesor went wrong bt i repeated and im getting same answer

Anyone in 2025?

Can I know how did you get determinent 30

Thank you professor

Best explanation, this was the step I knew before, many KZbinrs just making the whole process complicated 😑😑😑😑

I thought you said if they're moving in opposite directions, it's fo=fs×(V-Vo)/V+Vs. If so, that can't be the answer to the second question. Pls review the fo4mulas again.

the best explanation of 3x3 inverse matrix that i have ever watched thank you !!!!!!!!

yo made a mistake when substractes 5 from 21

O valor de determinante da matriz A é igual a 90, não 30 como apresentado pelo senhor professor. Tem de fazer a mesma operação para as linhas 2 e 3, depois somar todos os valores calculados. Obrigado.!

amazing understand to me

I didn't understand from 13:13 pls someone say how to do that from adding formula

Respect to you sir.🤝

when you multiply (2)^6-r to x^6-r what will it give you, another value right

THANK YOU MAN JUST THANK YOU❤

thanks

Thanks

Honestly this video has explained everything

Who else didn't realise the mistake 😂 but he understood the concept well 😂😂

The simplest method of an inverse of a three by three matrix...thank you so much

why don't we expand the denominator?

Thank you, Sir. There is a question ,it go like this. Express 2x squared plus x + 2 divided by (x squared+1) squared into a partial fraction.

Sir pls can you derive (a²+1/b²)(b²+1/a²) Where 'a' is alpha and 'b' is beta

100 and 200 is coming from where?

Where is that -2coming from?

Thank you so much sir God bless you 🙏

Thanks bro.

thank you🎉🎉🎉

You made an error on dy=15÷5=3