What are three irrational numbers between 4 and 5?

Answer 1

there can be many Irrational Numbers in between, infact there is infinity different ways,

here are 3

4.66666666666... In fraction is 4 2/3

4.44444444444... In fraction is 4 4/9

4.33333333333... In fraction is 4 1/3

Answer 2

Note: I am using root(number) for the square root of a number.

To the number 4, add any irrational number that is less than 1, for example root(2) / 2, root(3) / 2, pi / 4, etc.

Another option is to look for square roots between those numbers; the square root of almost any number between 16 and 25 (integer or otherwise) will do, e.g., root(17), root(18), root(16.1), etc. Specifically, if an integer is not a perfect square, its square root is irrational.