Here's a fascinating shortcut to squaring numbers that end in 5.

25^2 = (2*3*100) + 25 = 625

75^2 = (7*8*100) + 25 = 5,625

105^2 = (10*11*100) + 25 = 11,025

See the pattern? I never saw this correlation to numbers that end in .5

3.5^2 = 3*4 + .25 = 12.25

5.5^2 = 5*6 + .25 = 30.25

Someone was griping about an inability to calculate a square root and I realized there is a quick way to estimate 1/2 integer squares. It correlates to 1/4 integer squares, but the multiplicands become pretty large.

2.25^2 = 22*23/100 + 0.0025 = 5.0625


So something like
C*10^Z + 5*10^(Z - 1) has a shortcut

C*10^Z + 5*10^(Z - 1)
= C^2*10^(2Z) + 10*C*10^(2Z-1) + 25*10^(2Z-2)
= C^2*10^(2Z) + C*10^(2Z) + 25*10^(2Z-2)
= ( C^2 + C + 25*10^(-2) )*10^(2Z)
=( (C)(C + 1) + .25 )*10^(2Z)

It's a proof, but the shortcuts are so easy to remember.