Express the following in the form a+bi,
`sqrt(-8)`

Answer

To express \(\sqrt{-8}\) in the form \(a + bi\), we can follow these steps:

### Step 1: Rewrite the square root
We start with \(\sqrt{-8}\). We can express this as:
\[ \sqrt{-8} = \sqrt{-1 \cdot 8} = \sqrt{-1} \cdot \sqrt{8} \]

### Step 2: Use the imaginary unit
Recall that \(\sqrt{-1} = i\), where \(i\) is the imaginary unit. Thus, we can rewrite the expression as:
\[ \sqrt{-8} = i \cdot \sqrt{8} \]

### Step 3: Simplify \(\sqrt{8}\)
Next, we simplify \(\sqrt{8}\):
\[ \sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2} \]

### Step 4: Substitute back into the expression
Now, we substitute \(\sqrt{8}\) back into our expression:
\[ \sqrt{-8} = i \cdot 2\sqrt{2} = 2\sqrt{2}i \]

### Step 5: Write in the form \(a + bi\)
Finally, we express this in the form \(a + bi\):
\[ \sqrt{-8} = 0 + 2\sqrt{2}i \]
Here, \(a = 0\) and \(b = 2\sqrt{2}\).

### Final Answer
Thus, the final answer is:
\[ \sqrt{-8} = 0 + 2\sqrt{2}i \]

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