via The Irrationality of Problem: Prove that is an irrational number. Solution: The number, , is irrational, ie., it cannot be expressed as a ratio of integers a and b. To prove that this statement is t...

Here’s the proof. We start by assuming the square root of two, shown as sqrt(2) here, is equal to some fraction m/n. We intend to contradict this assumption: sqrt (2) = m/n (a fraction, reduced to its lowest ...