if I wanted to square 35, I would simply take 3 multiply by one greater(4) and slap 25 to the end. 3*4=12, *slap* 1225=35^2. works with all numbers ending with 5 and is a two second calculation.
15^5=1*2=2 *slap* 225
25^5=2*3=6 *slap* 625
45^5=4*5=20 *slap* 2025
55^5=5*6=30 *slap* 3025
65^5=6*7=42 *slap* 4225
how useful is this really? outside of numbers that are divisible by 10, I bet you can't square them easily. and for the numbers that are divisible by 10, the average of them ends with either a 5 or 0, which are easy to square to begin with.
why it works
let y end with a 5, then y=X5, ex. if y=135 then X=13.
y=X5
y=(2*X+1)*5
y^2= (2*X+1)^2*5^2
y^2=(4*X^2+4*X+1)*25
y^2=X*(X+1)*100+25
as for where to publish, nowhere becasue it is very common to add 0(add and substract the same thing to one side of an equation) and then rearrange the variables. same is true with multiplying by 1(multiply and divide by the same thing)