Question

By just examining the units digits, can you tell which of the following cannot be whole squares?
(i) 1026
(ii) 1028
(iii) 1024
(iv) 1022
(v) 1023
(vi) 1027

Answer 1

If the units digit of a number is 2, 3, 7 or 8, the number cannot be a whole square.
(i) 1026 has 6 as the units digit, so it is possibly a perfect square.
(ii) 1028 has 8 as the units digit, so it cannot be a perfect square.
(iii) 1024 has 4 as the units digit, so it is possibly a perfect square.
(iv) 1022 has 2 as the units digit, so it cannot be a perfect square.
(v) 1023 has 3 as the units digit, so it cannot be a perfect square.
(vi) 1027 has 7 as the unit digit, so it cannot be a perfect square.
Hence, by examining the units digits, we can be certain that 1028, 1022, 1023 and 1027 cannot be whole squares.