To approximate the value of $\sqrt{19}$, we can look at a number line and find two perfect squares that $\sqrt{19}$ is between. We know that $4^2=16$ and $5^2=25$, so $\sqrt{19}$ is between 4 and 5. To estimate the value, we divide the distance between 4 and 5 equally into 10 parts. Each part represents a value of 0.1 on the number line. Since $\sqrt{19}$ is closer to 4, we can estimate that $\sqrt{19}$ is approximately 4.3. Out of the answer choices, the closest option is $\boxed{\textbf{(D) }4.38}$.
