Simplify:
`(sqrt(-2))/(sqrt(-8))`

Answer

To simplify the expression \((\sqrt{-2})/(\sqrt{-8})\), we can follow these steps:

### Step 1: Rewrite the square roots of negative numbers
We know that \(\sqrt{-1} = i\), where \(i\) is the imaginary unit. Therefore, we can express the square roots of negative numbers as follows:
\[ \sqrt{-2} = \sqrt{-1} \cdot \sqrt{2} = i\sqrt{2} \]
\[ \sqrt{-8} = \sqrt{-1} \cdot \sqrt{8} = i\sqrt{8} \]

### Step 2: Simplify \(\sqrt{8}\)
We can simplify \(\sqrt{8}\) as:
\[ \sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2} \]
Thus, we have:
\[ \sqrt{-8} = i \cdot 2\sqrt{2} = 2i\sqrt{2} \]

### Step 3: Substitute back into the expression
Now, we can substitute these results back into the original expression:
\[ \frac{\sqrt{-2}}{\sqrt{-8}} = \frac{i\sqrt{2}}{2i\sqrt{2}} \]

### Step 4: Simplify the fraction
Now, we can simplify the fraction:
\[ \frac{i\sqrt{2}}{2i\sqrt{2}} = \frac{1}{2} \]
Here, \(i\) and \(\sqrt{2}\) in the numerator and denominator cancel out.

### Final Answer
Thus, the simplified form of \((\sqrt{-2})/(\sqrt{-8})\) is:
\[ \frac{1}{2} \]