Calculate: $\lim _{n\rightarrow \infty }{n}^{3/2}[\sqrt {{n}^{3}+3}-\sqrt {{n}^{3} -3}]$
What do the brackets mean? I know sometimes they are used to denote a function that returns only the integer part of a number, like $f(x) = [x]$ has values of $0$ on $(0,1)$ and then jumps to $1$ on [1,2) and then $2$ on $[2,3)$ and so on... Is this what is meant here?