IRRATIONALITY OF 2

This page deals with a proof that the (positive) square root of 2 is not a rational number. That is, sqrt(2) cannot be written in the form p/q where p and q are positive integers.

Proof:

By way of obtaining a contradiction, assume that there are positive integers p and q such that sqrt(2) = p/q.

The integers p and q can be chosen so as to have no common factors.

Then 2q² = p², and we use this equation to deduce that:

1. p is even

2. q is even

This means that p and q are both divisible by 2 - a contradiction

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