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The question in the image asks you to simplify the following expression and write the result in standard form:

\[
\sqrt{-3} \cdot \sqrt{-27}
\]

### Step 1: Simplify each square root involving negative numbers
When taking square roots of negative numbers, we can express them in terms of the imaginary unit \(i\), where \(i = \sqrt{-1}\).

\[
\sqrt{-3} = \sqrt{3} \cdot i
\]
\[
\sqrt{-27} = \sqrt{27} \cdot i = \sqrt{9 \times 3} \cdot i = 3\sqrt{3} \cdot i
\]

### Step 2: Multiply the simplified expressions
Now, multiply the two simplified expressions:

\[
(\sqrt{3} \cdot i) \cdot (3\sqrt{3} \cdot i) = \sqrt{3} \cdot 3\sqrt{3} \cdot i^2
\]

### Step 3: Simplify further
Since \(i^2 = -1\), the expression becomes:

\[
\sqrt{3} \cdot 3\sqrt{3} \cdot (-1) = 3 \cdot 3 \cdot (-1) = -9
\]

### Final Answer:
\[
\sqrt{-3} \cdot \sqrt{-27} = -9
\]

Let me know if you'd like more details or further clarification.

Here are 5 related questions for practice:
1. How would you simplify \(\sqrt{-4} \cdot \sqrt{-16}\)?
2. What is the standard form of \(\sqrt{-5} \cdot \sqrt{-20}\)?
3. If \(z = \sqrt{-9} \cdot \sqrt{-25}\), what is \(z\)?
4. How do you simplify \(\sqrt{-7} \cdot \sqrt{-49}\)?
5. What is the product of \(\sqrt{-2} \cdot \sqrt{-18}\)?

**Tip:** Always remember to use \(i = \sqrt{-1}\) when working with the square roots of negative numbers!

Simplify the expression √(-3) × √(-27) and write the result in standard form.

Learn how to simplify the expression √(-3) × √(-27) using complex numbers and imaginary units. This step-by-step solution covers key mathematical concepts like the properties of square roots and multiplication of imaginary numbers. Suitable for high school students in Grades 10-12.

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