Question

Is there any odd number whose square is even ?

Answer 1

Let n = 2n+1;  n is an integer here.

  we take n as an odd number.

n*n = (2m+1)^2 = 4m^2 + 4m + 1 = 4m(m+1) + 1

Clearly, 4m(m+1) is an even number, and (1 + even number) = odd number.

So the square of an odd number is always odd.