Which expression is equal to 2−√ 32 ?8i√2−8√28√2i−8i√2

Answer:A. [tex]8i\sqrt{2}[/tex]Step-by-step explanation:We have been given a radical expression [tex]2\sqrt{-32}[/tex]. We are asked to find equivalent expression to our given expression.Using radical rule [tex]\sqrt{-a}=\sqrt{-1}\cdot \sqrt{a}[/tex], we can write [tex]\sqrt{-32}[/tex] as product of [tex]\sqrt{-1}\cdot\sqrt{32}[/tex].[tex]2\sqrt{-32}=2\cdot \sqrt{-1}\cdot\sqrt{32}[/tex]Substitute [tex]\sqrt{-1}=i[/tex]:[tex]2\sqrt{-32}=2i\cdot\sqrt{32}[/tex][tex]2\sqrt{-32}=2i\cdot\sqrt{2\cdot 16}[/tex][tex]2\sqrt{-32}=2i\cdot\sqrt{2\cdot 4^2}[/tex][tex]2\sqrt{-32}=2*4i\cdot\sqrt{2}[/tex][tex]2\sqrt{-32}=8i\sqrt{2}[/tex]Therefore, the equivalent expression would be [tex]8i\sqrt{2}[/tex].