There are many other ways to attack the problem, the box method which is long and tedious, simple multiplication, calculator... otherwise if you know the perfect square expansion:
39^2 = (40 - 1)^2... mainly cos 40 and 1 and nice numbers to work with.
= (40)^2 - 2*(40)*(-1) + 1^2
= 1600 + 80 + 1
= 1681