text: What's wrong with it is that every number has two square roots. The validity of the manipulation √(xy) →√x√y is derived from the equality (xy)² = x²y². However, this equality also holds for (-xy)², so all you can really say about √x√y is that it is equal to ±√(xy). Thus, all you have managed to prove is that -1=±1, which is true, since -1=-1.