Prove that 3 root2 is irrational SolutionLets suppose 2 is a

Solution

Let\'s suppose ?2 is a rational number. Then we can write it ?2 = a/b where a, b are whole numbers, b not zero.

We additionally assume that this a/b is simplified to lowest terms, since that can obviously be done with any fraction. Notice that in order for a/b to be in simplest terms, both of a and b cannot be even. One or both must be odd. Otherwise, we could simplify a/b further.

From the equality ?2 = a/b it follows that 2 = a²/b², or a² = 2