Root 2

The square root of 2 is approximately 1.41421356237. It is an irrational number. Here is the proof:

Let's say that root 2 is rational and is equal to a/b, where a and b are relatively prime. Therefore, a^2/b^2=2. Then, a^2=2b^2, so a is even, and let a=2c. However, we get 4c^2=2b^2, which simplifies to 2c^2=b^2, meaning that b is also even, contradicting the assumption we made at the start. Therefore, root 2 is irrational.