Sqrt[ab]=Sqrt[a].Sqrt is not defined for imaginary numbers. Which is where this breaks down (your second line). Im sure you already knew that though. Heres one you may have already seen before...spot the breaking of fundamental maths laws...
Kinda, but kinda not. All I did was seperate the square root sign, but when taking the squareroot I took the wrong sign. Kinda like saying Sqrt[9] = -3