...Work out means training, why? For someone who dose not speak English very well it sounds like working outside.
Take out means to kill...
Work out may also mean deduce or calculate, as in "I need to work out the answer to this problem".
If you were to tell someone that you intend to take them out, they are rather more likely to ask where the two of you are going to eat. "Let me take you out to lunch", for example. You may have been thinking of the expression "take him out" as often used in action films.
As for learning English, most of the English-speaking world is still struggling with it on a daily basis if you ask me, so you should not worry too much!