By the difference of squares formula, we have $$\sqrt{4 + 1995 \cdot 1999} = \sqrt{4+ (1997 - 2)(1997 + 2) }= \sqrt{4 + ( 1997^2 - 4)} = 1997$$ Applying the same technique again leads to $$\sqrt{1+1995\cdot 1997}=\sqrt{1+(1996-1)(1996+1)}=\sqrt{1+(1996^2-1)}=\boxed{1996}$$