If the digit at unit place of a square number is 1, then it is a square of a number
whose unit place digit is either 9 or 1.
The square of a number 9 = 9 × 9 = 81
The square of 19 = 19 × 19 = 361
The square of 29 = 29 × 29 = 841
The square of 21 = 21 × 21 = 441
Therefore the unit place digit of a square root has to be either 9 or 1.