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!