The square root of $x$ is greater than 3 and less than 4. How many integer values of $x$ satisfy this condition?
I want to find all the integers $x$ such that $3 < \sqrt{x} < 4$. Squaring both sides of the inequality, I get $9 < x < 16$. Since $x$ has to be an integer, I can list the possible values: 10, 11, 12, 13, 14, and 15. There are 6 of them, so that's the answer. 