Question

Which is correct?
1. sqrt(-4) * sqrt(-16) = sqrt(-16*-4) = sqrt(64) = 8.
OR
2. sqrt(-4) * sqrt(-16) = 2i * 4i = 8i^2 = -8?

Answer 1

second one

Answer 2

why, is there something wrong with the first one?

Answer 3

only time
\[\sqrt{a}\sqrt{b}=\sqrt{ab}\] is if a and b are non-negative

Answer 4

\[\sqrt{-4}=2i\]
\[\sqrt{-16}=4i\]
\[2i\times 4i=8i^2=-8\]

Answer 5

wow I never knew that that the rule was for non-negative numbers only. But why is it for non-negative numbers only?

Answer 6

I mean if I didnt know about complex numbers then would the first one be correct?