Perfect Square Rules

Lets start with the simple rules previously discussed.

Any perfect square that ends in a 1 has a root of a number that ends in 9 or 1.

21²=441

19²=361

Any perfect square that ends in a 4  has a root of a number that ends in 2 or 8.

22²=484

18²=324

Any perfect square that ends in a 9  has a root of a number that ends in 3 or 7.

17²=289

33²=1089

Any perfect square that ends in a 0  has a root of a number that ends a 0.

20²=400

Any perfect square that ends in a 5  has a root of a number that ends a 5.

25²=625

Any number ending in 2,3,7, or 8 is not a perfect square.

√23 is not a perfect square
√38 is not a perfect square

Every perfect square except 1 is either a multiple of 3 one more than a multiple of 3:
25=8x3+1

169=56x3+1

144=48x3

225=75x3

Every perfect square except 1 is either divisible by 4 or is 1 more that a multiple of 4:

25=4x6+1

256=4x64

289=4x72+1

Every perfect square whose units digit is 5 always ends in 25. 

15²=225

215²=46225

I never thought rules would be so cool.