Now (1.4)2=1.96, so the number Ö2 is roughly 1.4. To get a better approximation divide 2 by 1.4 giving about 1.428, and take th e average of 1.4 and 1.428 to get 1.414. Repeating this process, 2¸1.414 » 1.41443 so 2 » 1.414 ×1.41443, and the average of these gives the next approximation 1.414215. We can continue this process indefinitely getting better approximations but never finding the square root exactly. If Ö2 were a rational number, that is if it could be written as a fraction p/q where p and q are integers, then we could find the exact value. The proof sorter shows that this number is IRRATIONAL. It is a proof by contradiction.