Translation:Please take a look at the menu.
If we want to give effect to the idiom presented in Chinese, it makes sense for us to recognize the construction "看一下" with an English idiom that's similar in tone and effect. Sure, "take/have a look at the menu" essentially means "look at the menu", but the latter is a bare imperative, and the former is modulated in tone and effect similarly to the Chinese expression.
It's not an exact science, and each sentence needs to be evaluated on its own terms, but since, in this case, the Chinese doesn't say "请看菜单", and English has a structure that can give effect to what it does say, it's logical that the English shouldn't say merely "please look at the menu".
It's wonderful that all of these native speakers of English are weighing in on whether "please look at the menu" is a correct English sentence (as if there were any doubt), and whether the meaning is basically the same, but again, some consideration of the entirety of the words in the Chinese sentence, and of the fuller exercise of learning and translation here on Duolingo, is part of the process as well.
It's subtle, but I do think there is a difference. "Take a look at the menu." seems to imply looking at the menu for a certain duration of time, whereas "Look at the menu" could be briefer, like, just glancing at it. From explanations I've read of Chinese, I think "take a look" is a good idiomatic translation of "看一下", in this context, because both imply a certain (possibly brief) duration.
"一下" is an adverbial, and it can be appended to a variety of verbs to indicate that the action is brief or casual. It's often shown in examples as coming directly after the verb, but it's technically independent and there are times when it sounds okay (and maybe even better) later in the sentence, e.g. in the phrase "帮我一下" .
I defer of course to native Chinese speakers, but to my mind "一下" is at least somewhat mobile.
Take a Look? Read, scan, browse, peruse. Are you literally 'taking' anything? I never understood why people use this verb - like saying 'take a dump' you don't take it, you leave it. The use of 'take' here is confusing.
At its root it's a matter of taking the time and the opportunity, however brief, to do something. And yes, you're literally taking something, which I say advisedly in consideration of the fact that "take" has 84 definitions in its transitive use alone, as listed here: http://www.dictionary.com/browse/take.
It has to be recognized that both "take a ..." and "... 一下" are idiomatic. The translation here isn't directly literal, but it's appropriate because it conveys a similar sense and tone.