Question

express the number in terms of (i).

(sqrt{-3})

(sqrt{-3} = \square) (simplify your answer.)

Explanation:

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<reasoning>

Identify the given expression

We are given the square root of a negative number:
\[\sqrt{-3}\]

Apply the product rule for radicals

Using the Product Rule for Radicals knowledge point
\[\sqrt{-3} = \sqrt{3 \cdot (-1)} = \sqrt{3} \cdot \sqrt{-1}\]

Substitute the imaginary unit

Using the Imaginary Numbers knowledge point
\[

$$\begin{aligned} &\sqrt{-1} = i\\ &\sqrt{3} \cdot \sqrt{-1} = \sqrt{3}i = i\sqrt{3} \end{aligned}$$

\]
</reasoning>

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

\(\sqrt{-3} =\) <blank>\(i\sqrt{3}\)</blank> (Simplify your answer.)
</answer>

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Answer:

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<reasoning>

Identify the given expression

We are given the square root of a negative number:
\[\sqrt{-3}\]

Apply the product rule for radicals

Using the Product Rule for Radicals knowledge point
\[\sqrt{-3} = \sqrt{3 \cdot (-1)} = \sqrt{3} \cdot \sqrt{-1}\]

Substitute the imaginary unit

Using the Imaginary Numbers knowledge point
\[

$$\begin{aligned} &\sqrt{-1} = i\\ &\sqrt{3} \cdot \sqrt{-1} = \sqrt{3}i = i\sqrt{3} \end{aligned}$$

\]
</reasoning>

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

\(\sqrt{-3} =\) <blank>\(i\sqrt{3}\)</blank> (Simplify your answer.)
</answer>

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