Which of the following approximates the square root of 19?

To approximate the square root of 19, it's helpful to consider the perfect squares that are close to this value. The perfect squares near 19 are 16 (which is (4^2)) and 25 (which is (5^2)). Hence, it is evident that the square root of 19 is between 4 and 5.

Calculating the square root more precisely, we find that (4.36) is a close approximation because (4.36^2) yields 19.0496, which is very close to 19. This indicates that (4.36) is indeed a reasonable estimation for the square root of 19.

The other options, while they may seem plausible at a glance, do not yield results as accurate as (4.36) when squared. The correct answer is supported by the mathematical findings surrounding these calculations, showing that (4.36) stands out as the most accurate choice.