On square roots and Geometric means Let $a$ and $b$ be two negative integers, say $-4$ and $-1$ 
So
$$\sqrt{ab}=\sqrt{-4\cdot(-1)}= + 2 $$
But then again,
$\sqrt{ab}$ is the geometric mean between $a$ and $b$, so it is supposed to lie between $a$ and $b$ that is between $-4$ and $-1$.
These two statements/results contradict each other...
Obviously i have messed up either of these two concepts and would be grateful if someone  could help me clear the same.. thank you

I always saw the geometric mean something similar to a distance formula: it is supposed to give you the distance of the mean, not the actual position of it per say (however when it is positive you get the position and distance :P ).
Think of it this way, if $\sqrt{(4)\cdot(1)} = 2$ and $\sqrt{(-4)\cdot(-1)} = 2$ then it must be the distance of the mean from 0 rather than the actual position of the mean itself (Even with imaginary numbers, you always refer to the roots using a positive i, never a negative i)
