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

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