The Square Root of Two cannot be expressed as a ratio between two integers; that is it is an irrational number.

Proof

Let us assume the converse that the Square Root of two can be expressed as the ratio of two numbers a and b. In that case there must be an a and b which are not both even as if they are both even we get the same ratio by dividing each by two until at least one of them is odd. Therefore if

a/b = SQRT (2) then
a²/b² = 2
a²= 2b² and
so a² is even and therefore a is even; so
a=2c for some c . Thus
a²= (2c)² and
a² = 4c²
2b² = 4c²
b² = 2c²
So b² is even and therefore b is even.
Therefore a and b are both even which is a contradiction.

Therefore the Square Root of Two cannot be expressed as the ratio between two integers.

QED.