False Proof of 1=-1

I found the following proof online and am confused as to where the error occurs.

$1=\sqrt{1}=\sqrt{(-1)(-1)}=\sqrt{-1}\sqrt{-1}=(\sqrt{-1})^2=-1$

My guess is that the error occurs here: $\sqrt{(-1)(-1)}=\sqrt{-1}\sqrt{-1}$, but I'm not sure how to show that.

Is my guess correct? How might I prove this?

Thank you!