Proof that √2 is Irrational

The diagonal of the square with side length of 1 is equal to √2. √2=1.414213562373095... the decimal representation of the square root of 2 doesn't have an end. But how do we know that?

[WdymAzulisntavalible]

This feels to high quality to be getting this few views.

[knu]

1. Radical 2
2. The square root of 2
3. Pythagoras’ constant

[BotturasStudios]

i learned this today as a freshman. very facinating

[serenitynow]

The square root of 2 is approximately equal to 577/408.

[AbhishekKumar-hkus]

1:26 at this moment only we can find the contradiction. Square numbers have odd numbers of factors.
2b^2 = a^2
b^2 and a^2 both have odd number of factors.
2b^2 means LHS have even number of prime factors and RHS have odd number of prime factors which is not possible according to fundamental theorem of arithmetics.

[Aadiweb]

banger vid.
the next vsauce/veritasium is here

[theepicone]

This video is a year old and somehow has 8 comments including replys. WHAT!