Multiply or divide.
-$\frac { \sqrt { - 64 } } { \sqrt { - 8 } }$
A) $2 \sqrt { 2 }$
B) $2 \mathrm { i } \sqrt { 2 }$
C) $- 2 \mathrm { i } \sqrt { 2 }$
D) $- 2 \sqrt { 2 }$

Question

Quizplus · Accepted Answer

The square root of a negative number involves the imaginary unit $i$, where $i = \sqrt{-1}$. Thus, $\sqrt{-64} = 8i$ and $\sqrt{-8} = 2i\sqrt{2}$. Dividing these gives $\frac{8i}{2i\sqrt{2}} = 4/\sqrt{2} = 2\sqrt{2}$, since the $i$ terms cancel out.

Multiply or Divide −64−8\frac { \sqrt { - 64 } } { \sqrt { - 8 } }−8​−64​​

Multiply or Divide $\frac { \sqrt { - 64 } } { \sqrt { - 8 } }$