The square root of h is greater than 10/3 and less than 24/5. How many integer values of h satisfy this condition? I think the first step would be to square each fraction so 100/9 and 576/25 and then see which whole numbers are between. Am I on the right track?

Answer 1

yes

10/3 < √x < 24/5
square it
100/9 ≤ x ≤ 576/25
11.111.. < x < 23.04

so with whole numbers ...
{ 12, 13, ... 22, 23}

count them up

(just realized I used x instead of h, no big deal, eh)