C3: intuitively knowing the values of nature logs and e

Hi everyone,

I'm going through a number of questions on natural logs and the number 4. For example:

$e^{ \frac{ln9}{2}}$ and $e^{ \frac{ln4}{2}}$

The answers are nice whole numbers that have links to the original numbers in the logs (such as $e^{ \frac{ln9}{2}}$ being the square root of 9, and $e^{ \frac{ln4}{2}}$ being the square root of 4. I'm getting the answers by just punching the numbers in my calculator. Aside from familiarity, should I be recognising what these numbers are without using my calculator, or is the calculator the only way to go?