Question

By just examining the units digits, can you tell which of the following cannot be whole squares?
1028

Answer 1

Hint: As we know that the numbers having 2,3,7,8 as it’s a unit digit, then the number is not a whole square of any of the numbers. So, just check the unit digit of the given number and note the number obtained, then we check if the number is amongst 2,3,7,8, if yes then the number is not a perfect square of any number.

Complete step by step answer:

The given number is 1028.
As we know that the numbers having 2,3,7,8 as it’s a unit digit, then the number is not a whole square of any of the numbers.
So, here the end digit is 8. Hence, it matches the 2,3,7,8 and so we can see that the number given is not the whole square of any of the numbers.

Note: If the units digits are 1, 4, 5, 6, 9 then the number will be a whole square, as we know that \[{1^2} = 1\], \[{2^2} = 4\], \[{3^2} = 9\], \[{4^2} = 16\], \[{5^2} = 25\], \[{6^2} = 36\], \[{7^2} = 49\], \[{8^2} = 64\], \[{9^2} = 81\]. So, as we can clearly see that the units place are always amongst 1, 4, 5, 6, and 9, for perfect square numbers. So we can say that if a number has units place as 2, 3, 7, 8 then the number is not a perfect square.