Alright, so what you do is take an irrational number, like π, and get it between 7.7 and 7.9. How? For example, if you wanted to get π between 10 and 10.1, we know that π is 3.14 something. If we added 6.9 to it,we'd have 10.04 something. Since the numbers after that 1, 0, and 0 are not changed, this is still irrational as you can still not represent π with integers. For example, if we had π/1, we can add 5/1 to it and we'd have (π+5)/1, which can be separated into π/1+5/1 - a irrational number added to a rational number is not rational (The proof for this can be learned in calculus). Good luck, and feel free to ask with further questions!
