Demonstrate that 4k + 3 cannot be perfect square

Question

I wonder if it can be mathematically demonstrated that

4k + 3 != n^2 where k,n are N (natural) numbers?

My daughter (6's grade) has a problem and the book's answer is just enumerating k elements

{3,7,11,19,23,27...}

saying that they cannot be perfect square.

Thank you,

Answer 1

Hint: the square of an even number is $(2m)^2 = 4m^2 = 4k$.

The square of an odd number is $(2m+1)^2 = 4m^2 +4m+1 = 4k + 1$.

Can you finish?