Question

Square root of negative 400

Answer 1

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