Question

Simplify square root of negative 48

Answer 1

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