The square root of $x$ is greater than 2 and less than 4. How many integer values of $x$ satisfy this condition?
I need to find the integers $x$ that make $\sqrt{x}$ lie between 2 and 4. I can start by squaring both sides of the inequality: $\sqrt{x} > 2 \implies x > 4$ and $\sqrt{x} < 4 \implies x < 16$. So I have $4 < x < 16$, and I need to count how many integers are in this interval. I can exclude 4 and 16, since they are not strictly in the interval, and I can list the remaining integers: 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, and 15. There are 11 of them, so that's my answer. 