Question

How do you know that 50 is not a perfect square?

Answer 1

We can always do a prime factoring of it, and check

50 = 2*5*5
        2*5²

a perfect square, so-called, is the resulting number of a squared value, well 50 is not the result of anything squared, is the result of 3 factors, in this case 2,5 and 5.

a perfect square will be something like say 64, or 144, because

64 = 8*8
        8²

144 = 12*12
          12²