Get confused with the use of "go"

You should go take a shower.
Go take a nap!

Those are right and so are you. Those are imperative sentences, and 'go take' is a short form of 'go and take':

You should go and take a shower.
Go and take a nap!

Thank you for the explanation above. I have another question, how if i want to use go and buy in affirmative clause.
The sentence: I will go buy some food OR I will go buying some food. Which one is correct in formal sentence?

Well, none is particularly formal, since food shopping is a very informal activity, but we say this:

I'll go (and) buy some food.

If both actions are meant, use 'go' + 'do' (infinitive).
If only the second action is meant, use 'go' + doing (-ing form). This form we use only with actions that include movement, so we can go skiing, go shopping, go bowling, go running

The verb "go" can be followed by a gerund, but not always. Here are some examples of usage:

I will go fishing tomorrow.

I will go fish tomorrow.

I will go to the fishing hole tomorrow.

I will go and fish tomorrow.

Do you want to go fishing tomorrow? Yes, I can go for fishing (that is, going fishing is acceptable to me) tomorrow.

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