Dr. Pepper,
The math for x+0.5 works like this:
x*(x+1)=x^2+x
and
(x+0.5)^2=(x+0.5)*(x+0.5)=x^2+0.5x+0.5x+0.5*0.5=x^2+x+0.25
So the square is 0.25 larger than the other product.
I did figure out the math when my daughter told me the trick because she was younger then and used smaller numbers, so I wanted to prove it would work for all numbers.
Thanks for the proof for squares of numbers ending in 5. I’d heard of that but didn’t know why it worked.
Note to mod: Would you please delete my previous reply to Dr. Pepper? I hit “send post” too soon. Thanks.