Answer
$14.142i$
Work Step by Step
Step 1: $\sqrt {-200}$
Step 2: $\sqrt {-1\times200}$
Step 3: $\sqrt {-1}\times\sqrt {200}$
Step 4: $\sqrt {-1}\times\sqrt {2\times100}$
Step 5: $\sqrt {-1}\times\sqrt 2\times\sqrt {100}$
Step 6: As $i=\sqrt {-1}$,$\sqrt {-1}\times\sqrt 2\times\sqrt {100}=i\times\sqrt 2\times10$.
Step 7: $i\times10\times\sqrt 2=10i\sqrt 2\approx14.142i$
