Questions: Write the number as the product of a real number and i. sqrt(-9)

Transcript text: Write the number as the product of a real number and $i$. \[ \sqrt{-9} \]

Solution

Step 1: Express the square root of a negative number

The square root of a negative number can be expressed using the imaginary unit $ i $, where $ i = \sqrt{-1} $.

Step 2: Rewrite the expression

Rewrite $ \sqrt{-9} $ as $ \sqrt{9 \cdot (-1)} $.

Step 3: Separate the square roots

Separate the square roots into $ \sqrt{9} \cdot \sqrt{-1} $.

Step 4: Simplify the expression

Simplify $ \sqrt{9} $ to $ 3 $ and $ \sqrt{-1} $ to $ i $, resulting in $ 3i $.

$\boxed{3i}$

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