This method of proof can easily be generalised to prove that Ön is irrational when n is not a square number.

What is the length of the diagonal of a square with sides of length 2?
How do we find the value of Ö2?
What number has 2 as its square?
What is the side of a square which has area 2?
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 the 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 so we cannot find an exact value.