homework-6

Question

Answer 1

Using Direct Proof : Let’s assume n = a*a and m = b*b where a and b are some integers.

m+n+2$\sqrt{}$mn = a*a + b*b + 2ab = (a+b)$^{2}$ i.e., (some integer)$^{2}$.

Therefore m+n+2$\sqrt{}$mn is a perfect square.