Question

what is a rational number that is between 5.2 and 5.5. what is a irrational number that is between 5.2 and 5.5.

Answer 1

5.2 < x < 5.5
square
5.2² < x² < 5.5²
27.04 < x² < 30.25
Pick any number for between 27.04 and 30.25 for x², as long as it's not a perfect square. So you could pick 30.

x² = 30

x = √30 → irrational number between 5.2 and 5.5