And that’s where I’m not sure what “natural” means… can’t really be the way it was first taught in school because different countries teach things differently all the time; just compare long division US vs France vs Germany.
I for one would use 50 instead of 70 for 68 as describes in this post:
If you’re curious… same steps as in the example but with a delta of 18 (68-50) for a lhs of 25+18 and a rhs of 18 squared.
I don’t consider this a shortcut or anything that wouldn’t be a “natural” way of calculating this because it builds on top of the up to 25 symmetry for the squares… you can read the rest of the linked post for details.
However, I wouldn’t insist on this method if we were talking about 65 instead of 68. In this case the tenth digits are the same and the unit digits add to 10, so you just multiply the unit digits for the rhs (5x5=25) and multiply the tenth digit with itself plus one (6x7=42) for the lhs… 4225. Essentially, my method of choice for any 2-digit square that ends in 5.
Maybe it’s just me but I like to use a solution that fits the problem… surely you can hammer a screw into the wall almost as easily as a nail, but for me, a screw asks for a screwdriver not a hammer.