Question

Which of the following number can never be a perfect square?

• A. 169_0
• B. 6_ _1
• C. 7 _ _8
• D. 9_ _6

Answer 1

The correct option is C 7 _ _8

If we see the unit digit of the perfect square of the numbers from 1 to 10 then we will observe that perfect square end in 0, 1, 4, 5, 6 and 9.

$1^2$ =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
${10}^2$ = 100

And the unit digit of perfect square keeps repeating like the above ones from 11 on wards. So, any perfect square will have its unit's place digit as either 0 or 1 or 4 or 5 or 6 or 9.
In 7_ _ 8, the unit's place is 8. Hence, it can never be a perfect square.