A four digit number is a complete square number, and the first two digits are equal, and the last two digits are equal? Please answer in detail, and tell me what is a complete square?

A four digit number is a complete square number, and the first two digits are equal, and the last two digits are equal? Please answer in detail, and tell me what is a complete square?

If a number is the complete square of another integer, then we call it a complete square number, also called a square number
0,1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,256,289,324,361,400,441,484,…
Four digits can be expressed as
a×1000＋a×100＋b×10＋b
＝a×1100＋b×11
＝11×（a×100＋b）
Because a × 100 + B must be divisible by 11, a + B = 11
Four digit = 11 × (a × 100 + (11-A))
＝11×（a×99＋11）
＝11×11×（9a+1)
As long as 9A + 1 is a perfect square
It is verified by a = 2, 3, 4, 5, 6, 7, 8, 9,
9a＋1＝19、28、27、46、55、64、73.
So there is only one solution for a = 7; b = 4
So the four digit number is 7744 = 11 ^ 2 × 8 ^ 2 = 88 × 88