"Check" or "check out" or "check on"?

Mary was very busy. That, however, didn't stop her from checking (on/out) Mrs. Johnsons' research.

Is it necessary to add on or out in cases like this? If so, why?

Mary was very busy. That, however, didn't stop her from checking Mrs. Johnson’s research.
Mary was very busy. That, however, didn't stop her from checking out Mrs. Johnson’s research.

These both mean that Mary reviewed Mrs. Johnson's research.

But when you say:

Mary was very busy. That, however, didn't stop her from checking on Mrs. Johnson’s research.

this means Mary checked on the status/progress of Mrs. Johnson's research, but not the contents of it.