Questions: Simplify. -√(-40) (A) -i √10 (B) i √10 (C) -2 i √10 (D) 2 i √10

Simplify. -√(-40) (A) -i √10 (B) i √10 (C) -2 i √10 (D) 2 i √10
Transcript text: Simplify. \[ -\sqrt{-40} \] (A) $-i \sqrt{10}$ (B) $i \sqrt{10}$ (C) $-2 i \sqrt{10}$ (D) $2 i \sqrt{10}$
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Solution

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Solution Steps

Step 1: Rewrite the expression

The expression is \(-\sqrt{-40}\). Since the square root of a negative number involves the imaginary unit \(i\), we rewrite \(\sqrt{-40}\) as \(i\sqrt{40}\).

Step 2: Simplify the square root

Simplify \(\sqrt{40}\) by factoring it into \(\sqrt{4 \cdot 10}\). This becomes \(2\sqrt{10}\).

Step 3: Combine the terms

Substitute the simplified square root back into the expression: \(-i \cdot 2\sqrt{10}\). This simplifies to \(-2i\sqrt{10}\).

Step 4: Match with the given options

The simplified expression \(-2i\sqrt{10}\) matches option (C).

Final Answer

\(\boxed{-2 i \sqrt{10}}\)

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