sqrt-1

if sqrt(2)*sqrt(8) = sqrt(2*8) why isnt sqrt(-1)*sqrt(-1)=sqrt(-1*-1)

\(if\;\; \sqrt2*\sqrt8= \sqrt{2*8}\\\text{ why isn't }\quad\\ \sqrt{-1}*\sqrt{-1}=\sqrt{-1*-1}\)

The rules for real numbers often do not extend to imaginary numbers. 

This is one such case.

Alan, or someone else might be able to give a better explanation.   :/

sqrt((-1)*(-1)) = +/-1

The rule is

√a  *  √b   =   √ [ a * b]   only if a, b  ≥  0