The following numbers are not perfect squares. Give reasons?

257

Given a number 257 is not perfect square. Need to find out the reason.

Now, we have the perfect square = , where m and n are integers

⇒257 is not a perfect square as it cannot be expressed as n × n form the product of two equal

integer and the number that have 2,3,7 or 8 in the units place are not perfect squares.

Hence, the given number 257 is not a perfect square.