Dangerous calculate in your head -tips

I’ve been exposed to some calculate big numbers in your head -tips in social media. At first, I thought that’s nice. It’s good mental practice to use one’s own brain instead of calculator. But then when I look closer, I see that some of them are poorly defined.

Here is an example of squares of large numbers: 102 x 102 = 10404. The tip says: take the original number and add the last digit to it, so 104. Then, take the last digit and square it, use two digits. That means 04. Now these to should be concatenated like this: 10404. Seems to work. But the important question is when you can use this in the first place? There is no range mentioned in the tip.

Ok, you can say that this works for numbers 101,…,109. If you really want to make an effort and memorize this rule for those calculations, go for it. But I see a real danger that students are not so punctilious that they check all these tips before using them on any numbers (greater that 100.) This is bad for credibility of well formulated tips, too.

Best regards,
Concerned Math Teacher.