Question

how do I Simplify the following expression; express in terms of i. sqrt -54

Answer 1

\[\sqrt{-54}\]
re write the \(-54\) as a product of factors
\(-54=-1\times54=-1\times6\times9=-1 \times2\times3^3\)

\[\sqrt{-54}\rightarrow\sqrt{-1 \times2\times3^3}\]

Answer 2

\[\sqrt{-1 \times2\times3^3}=\sqrt {-1}\times\sqrt 2\times\sqrt{3^3}\]\[=\sqrt {-1}\times\sqrt 2\times\sqrt{3\times3^2}\]\[=i\times\sqrt 2\times3\sqrt{3}\]\[=3\sqrt6i\]

Answer 3

ok thank you I had up to the i x correct then i messed it up I see how you got it appreceiate it thank you