Question

Simplify square root of negative 48

Answer 1

`\bf √(-48)\qquad \begin{cases} 48=2\cdot 2\cdot 2\cdot 2\cdot 3\\ \qquad 2^2\cdot 2^2\cdot 3\\ \qquad (2^2)^2\cdot 3 \end{cases}\implies √(-1\cdot (2^2)^2\cdot 3) \\\\\\ √(-1)\cdot √((2^2)^2\cdot 3)\implies i\cdot 2^2√(3)\implies 4√(3)\ i`