Question

Which of the following number is squares of even number ?

256

Answer 1

The numbers whose last digit is odd can never be the square of even numbers. 

For each number, use prime factorisation method and make pairs of equal factors. 

256 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
             = (2 x 2) x (2 x 2) x (2 x 2) x (2 x 2)
There are no factors that are not paired. Hence, 256 is a perfect square. The square of an even number is always even. Hence, 256 is the square of an even number.