Question

express the number in terms of \\(i\\).

\\\sqrt{-45}\\

\\(\sqrt{-45} = \square\\)
(simplify your answer. type an exact answer, using radicals and \\(i\\) as needed.)

Explanation:

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<reasoning>

Separate the negative sign

Using the Imaginary Numbers knowledge point
\[
\sqrt{-45} = \sqrt{-1 \cdot 45} = \sqrt{-1} \cdot \sqrt{45} = i\sqrt{45}
\]

Simplify the radical

Using the Product Rule for Radicals knowledge point
\[
\sqrt{45} = \sqrt{9 \cdot 5} = \sqrt{9} \cdot \sqrt{5} = 3\sqrt{5}
\]

Combine the results

Using the Imaginary Numbers and Product Rule for Radicals knowledge points
\[
\sqrt{-45} = 3i\sqrt{5}
\]
</reasoning>

<answer>
Express the number in terms of \(i\).

\(\sqrt{-45} =\) <blank>\(3i\sqrt{5}\)</blank>
</answer>

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"question_type": "Fill-in-the-blank",
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"Mathematics",
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"Imaginary Numbers"
]
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Answer:

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</pre_analysis>

<reasoning>

Separate the negative sign

Using the Imaginary Numbers knowledge point
\[
\sqrt{-45} = \sqrt{-1 \cdot 45} = \sqrt{-1} \cdot \sqrt{45} = i\sqrt{45}
\]

Simplify the radical

Using the Product Rule for Radicals knowledge point
\[
\sqrt{45} = \sqrt{9 \cdot 5} = \sqrt{9} \cdot \sqrt{5} = 3\sqrt{5}
\]

Combine the results

Using the Imaginary Numbers and Product Rule for Radicals knowledge points
\[
\sqrt{-45} = 3i\sqrt{5}
\]
</reasoning>

<answer>
Express the number in terms of \(i\).

\(\sqrt{-45} =\) <blank>\(3i\sqrt{5}\)</blank>
</answer>

<post_analysis>
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