Problem 174

Using a calculator, $\sqrt{15} \approx 3.87$ and $\sqrt{50} \approx 7.07$.

The integers between these real numbers are $4$, $5$, $6$, $7$, of which there are $4$.

Alternatively, we could note that integers between $\sqrt{15}$ and $\sqrt{50}$ correspond to values of $\sqrt{n}$ where $n$ is a perfect square and $n$ is between $15$ and $50$. The perfect squares between $15$ and $50$ are $16$, $25$, $36$, $49$, of which there are $4$.