Question

simplify imaginary number
5times square root of negative 48

Answer 1

\(\bf 5\sqrt{-48}\\ \quad \\ \quad \\
\color{green}{-48 = 2\cdot 2\cdot 2\cdot2\cdot-3\implies 2^2\cdot 2^2\cdot 3\implies (2^2)^2\cdot -3}\\ \quad \\
5\sqrt{-48}\implies 5\sqrt{(2^2)^2\cdot -3}\implies 5\cdot 2^2\sqrt{-3}\implies 5\cdot 4\sqrt{3\cdot -1}\\ \quad \\
20\sqrt{3}\cdot\sqrt{-1}\implies 20\sqrt{3}\quad i\)