Let's put the sets into words:
Set A is all real x values less than 3; set B is all real x values of at least -√3.
Picture two number lines, one for set A and one for set B. This lines are aligned so that their zero points are in line and the negative numbers lie on the left of the zero point and positives on the right (including zero).
A⋃B is set A combined with set B. The two lines overlap between -√3 and 3; combining the sets means that A takes care of values of x below -√3 and B takes care of everything above 3, so between them all real values are covered and this is simply {x∈R}. A⋃B={x∈R}.
I assume A/B means A difference B (normally written A\B). This is all A except for those elements which are in B. This means values of x less than -√3, because what's above is in set B. A\B={x∈R | x<-√3}.
B\A={x∈R | x≥3} that is, values of x between -√3 and 3 (exclusive) are excluded, so we have to include x=3 which is not in A.
A⋂B is all the elements that A and B have in common: A⋂B={x∈R | -√3≤x<3}.