Any whole number ends in its ones place digit.
The square of a whole number ending in 0 ends in 0
The square of a whole number ending in 1 ends in 1.
The square of a whole number ending in 2 ends in 4.
The square of a whole number ending in 3 ends in 9.
The square of a whole number ending in 4 ends in 6.
The square of a whole number ending in 5 ends in 5.
The square of a whole number ending in 6 ends in 6.
The square of a whole number ending in 7 ends in 9.
The square of a whole number ending in 8 ends in 4.
The square of a whole number ending in 9 ends in 1.
So all square numbers end in 0,1,4,5,6, or 9.
They never end in 2,3,7, or 8.
Edwin