What number between 7.7 and7.9 is irrational?

Answer 1

Take any irrational number - e.g., square root of 2, cubic root of 5, pi, e, etc. - and divide it by an integer (1) that is large enough, so that the result is smaller than the difference (which in this 0.2). Add that to 7.7.Note 1: Actually, any rational number will do here.

Answer 2

Consider

7.700000000000000000000001

7.7000000000000000000000011

7.7000000000000000000000012

7.7000000000000000000000013

7.700000000002

and so on.

Similarly, between any two of these there are infinitely many rational numbers.

Answer 3

7.8