Question

Square root of negative 400

Answer 1

$i=\sqrt{-1}\\\\\sqrt{a}=b\iff b^2=a\ for\ a\geq0\ and\ b\geq0\\\\\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\-------------------------------\\\\\sqrt{-400}=\sqrt{(400)(-1)}=\sqrt{400}\cdot\sqrt{-1}=20\cdot i=\boxed{20i}\\\\\sqrt{400}=20\ because\ 20^2=400$