Answer
$8.660i$
Work Step by Step
Step 1: $\sqrt {-75}$
Step 2: $\sqrt {-1\times75}$
Step 3: $\sqrt {-1}\times\sqrt {75}$
Step 4: $\sqrt {-1}\times\sqrt {3\times25}$
Step 5: $\sqrt {-1}\times\sqrt 3\times\sqrt {25}$
Step 6: As $i=\sqrt {-1}$,$\sqrt {-1}\times\sqrt 3\times\sqrt {25}=i\times\sqrt 3\times5$.
Step 7: $i\times5\times\sqrt 3=5i\sqrt 3\approx8.660i$