One Equals Minus One

Resolution
This is a falsidical paradox arising from incorrect reasoning about the nature of square roots.

Explanation
The property:
 * $\sqrt {a} \times \sqrt {b} = \sqrt {ab}$

can only be used when:
 * $a \ge 0$ and $b \ge 0$

Since $-1 < 0$, this property of square roots cannot be applied to this statement.

This is how the analysis is to go:

... and all is well with the world.

Also see

 * Complex numbers