Explain why 2 + √ 3 is an irrational number.

The number 2+√3 is irrational, it cannot be expressed as a ratio of integers a and b. To prove that this statement is true, let us Assume that it is rational and then prove it isn't (Contradiction).

So the Assumptions states that:

(1) 2+√3

Where a and b are 2 integers

Now since we want to disapprove our assumption in order to get our desired result, we must show that there are no such two integers.

Squaring both sides give:

3=a/b

3=a^2 / b^2

what two number time itself (twice) can be divide by another number time itself (twice) to get 3