Answer:
[tex]\sqrt{59}[/tex]
Step-by-step explanation:
7^2 is 49 and 8^2 is 64, which means the square root of any number between 49 and 64 (exclusive) will be in between 7 and 8, and it's also going to be irrational, because it's not a perfect square.
One number between 49 and 64 is 59, so [tex]\sqrt{59}[/tex] is an irrational number between 7 and 8