To determine the result of multiplying \(-\sqrt{-8}\) and \(4545\), we first need to simplify \(-\sqrt{-8}\).
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\(-\sqrt{-8}\) can be rewritten using the imaginary unit \(i\): \[ -\sqrt{-8} = -\sqrt{8} \cdot \sqrt{-1} = -\sqrt{8} \cdot i = -\sqrt{4 \cdot 2} \cdot i = -2\sqrt{2} \cdot i \]
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Now we multiply this by \(4545\): \[ 4545 \cdot (-2\sqrt{2} \cdot i) = -9090\sqrt{2} \cdot i \]
The result is \( -9090\sqrt{2} i \), which is a complex number, specifically an imaginary number.
Now, looking at your options:
- An integer
- An irrational number
- A rational number
- The number zero
Since the result is not a real number and is specifically a complex number, none of these options accurately describe the result. If we strictly adhere to the types provided, the closest would be "an irrational number," but it is important to note that the outcome is a complex number, which is not included in your provided responses.
However, given your options, the correct classification of the imaginary part can be considered as "an irrational number" in the context of the square root being part of the number, but this is not definitive since it is combined with 'i.'
In conclusion, while an imaginary number is the best description of the product, among the options provided, you might select "an irrational number" as the answer.
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