Proof of Irrationality

In this video we look at how to prove that the nth root of any prime number, p is always irrational. For example, nth root of 2, 3, 5, 7, ... and so on.

The proof technique demonstrated here is Proof by Contradiction.

Also, the proof demonstrates some fundamentals of number theory.

Category:

Education

Tags:

• math
• mathematics
• calculus
• derivative
• differentiation
• pollardrho06
• shahz
• number theory
• proof
• irrationality

[ZeeNwar]

Does a similar proof hold for complex(Gaussian) primes?

[pollardrho06]

Will look into it and get back with you.

[draconisthe0ry]

this song is lame . . .

[themathematician1]

If p|a and p|b then p|(an + bm) for some integers n and m. but since (a,b) =1 then an+bm = 1, so p|(an+bm) = 1. Notice that p is prime and p>1 so, p|1 leads to a contradiction. Hence p^(1/n) is irrational.

[raneboy13]

all i understood was the happy faces with = >

[200609]

I CAME!!!

[luked82]

Very cool. I followed for the first minute or two. It has been a couple of years since number theory for me. How are your Calc skills? I have a problem for you to solve. You can find the problem at the end of my video called String Art is Calculus.

[BobbyHil]

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