Question

what is the simplified form of 8 times the square root of -27?

Answer 1

So we have:
\[
8\sqrt{-27}=8\sqrt{-(9)(3)}=8\sqrt{-(3^2)(3)}=8(3)\sqrt{-3}=24\sqrt{-3}
\]We know that:
\[
i^2=-1
\]So:
\[
24\sqrt{-3}=24i\sqrt{3}
\]Which is your final answer.