"Let's take a look this word here." is not a correct sentence. "Let's take a look at this word here.", on the other hand, is a correct sentence, due to the use of "at". While using "take a look at", we are using the same grammar as if we wereonly using "look at". So, for example, you could say "Look AT this cat", but you couldn't say "Look this cat". It's the same with "take a look at". Examples: "Come and take a look at this book.", "Hurry, take a look at this essay for me.". The only instance where you could use "take a look" by itself, without the "at", would be when you are not saying anything after it in a sentence. So, for example, you can say "Come, take a look" or "Can you take a look?". In these cases, you wouldn't use "at", but this is the ONLY situatiton. Hope this helps!