According to Excursions in Mathematics by Ogilvie (Dover) Joseph Louis LaGrange (1736-1813) expressed the proof of the irrationality of the square root of 2, in a handy sentence:

It (square root of 2) cannot be found in fractions, for if you take a fraction reduced to its lowest terms, the square of that fraction will again be a fraction reduced to its lowest terms and consequently cannot be equal to the whole number 2.I think that is interesting and related to the other proofs presented.

# The square root of any prime number is irrational (idea)

See all of The square root of any prime number is irrational, there are 3 more in this node.

(idea) | by uncljoedoc |
Sat Dec 09 2006 at 17:08:21 |