Does $\sqrt{i^4} = i^2$? I'm assuming it doesn't, because if it did, then $1 = \sqrt{1} = \sqrt{i^4} = i^2 = -1$. In general, does $\sqrt{x^4} = x^2$?

In general,
$$\sqrt{x^2} = \pm x$$
so technically, 
$$\sqrt{i^4} = \pm i^2$$
so what you gave is one of the possible solutions.
