Question

Simplify this using the imaginary i

Answer 1

`\bf √(-200)\implies √(-1\cdot 200)\implies √(-1)\cdot √(200)\quad \begin{cases} √(-1)=i\\ 200=5\cdot 5\cdot 8\\ \qquad 5^2\cdot 8 \end{cases} \\\\\\ i√(5^2\cdot 8)\implies i\cdot 5√(8)\implies 5i√(8)\\\\ -------------------------------\\\\ \textit{by the way }8=2^2\cdot 2\qquad 5i√(2^2\cdot 2)\implies 5i\cdot 2√(2)\implies \boxed{10i√(2)}`

Answer 2

200=25*8, 25=5^2, therefore, the answer is 5iroot8( the second one)