1. The problem is to evaluate the expression $\sqrt{19}$. 2. The square root function $\sqrt{x}$ gives the positive number which, when squared, equals $x$. 3. Since 19 is not a perfect square, $\sqrt{19}$ is an irrational number. 4. We can approximate $\sqrt{19}$ by finding the nearest perfect squares: $16$ and $25$, whose roots are $4$ and $5$ respectively. 5. Since $19$ is closer to $16$, $\sqrt{19}$ is slightly more than $4$. 6. Using a calculator or estimation, $\sqrt{19} \approx 4.3589$. Therefore, the value of $\sqrt{19}$ is approximately $4.3589$.