Divide.
-$\frac { \sqrt { - 1000 } \sqrt { - 8 } } { \sqrt { - 25 } }$
A) $8 \sqrt { 5 }$
B) $- 8 i \sqrt { 5 }$
C) $- 8 \sqrt { 5 }$
D) $8 i \sqrt { 5 }$

Question

Quizplus · Accepted Answer

The expression simplifies as follows: $\frac{\sqrt{-1000} \cdot \sqrt{-8}}{\sqrt{-25}} = \frac{\sqrt{1000} \cdot i \cdot \sqrt{8} \cdot i}{\sqrt{25} \cdot i} = \frac{10i \cdot 2\sqrt{2}i}{5i} = \frac{20i^2\sqrt{2}}{5i}$. Since $i^2 = -1$, this simplifies to $\frac{-20\sqrt{2}}{5i} = -4\sqrt{2} \cdot \frac{-i}{i} = 4\sqrt{2}i$. Converting $\sqrt{2}$ into $\sqrt{4}\sqrt{2}$ gives $4\sqrt{4}\sqrt{2}i = 8\sqrt{2}i$, which is not directly matching any option. Correcting the simplification process: $\frac{\sqrt{-1000} \cdot \sqrt{-8}}{\sqrt{-25}} = \frac{10\sqrt{10}i \cdot 2\sqrt{2}i}{5i} = \frac{20i^2\sqrt{20}}{5i} = 4\sqrt{20}i = 8\sqrt{5}i$, which matches option D.

Divide - −1000−8−25\frac { \sqrt { - 1000 } \sqrt { - 8 } } { \sqrt { - 25 } }−25​−1000​−8​​

Divide
- $\frac { \sqrt { - 1000 } \sqrt { - 8 } } { \sqrt { - 25 } }$