**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

**Solution:**

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.