To express the square root of $\sqrt{-45}$ as the product of two square roots, you can break it down as follows:

$\sqrt{-45} = \sqrt{-1 \times 45}$

Now, using the property of square roots that $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$, you can split this into:

$\sqrt{-45} = \sqrt{-1} \times \sqrt{45}$

Since $\sqrt{-1} = i$ (the imaginary unit), we have:

$\sqrt{-45} = i \times \sqrt{45}$

Thus, the square root of $-45$ is written as $i \times \sqrt{45}$, which is the product of two square roots.

Would you like to explore more details on this, or do you have any questions?

Here are 5 related questions to explore:

1. How do you simplify $\sqrt{45}$?
2. What is the value of $\sqrt{-1}$ and why is it called imaginary?
3. Can all negative square roots be written as a product of $i$ and a positive square root?
4. How do you multiply two complex numbers like $3i \times 2i$?
5. What is the significance of the imaginary unit $i$ in mathematics?

Tip: When simplifying square roots, try to factor the number into its prime factors to make simplifications easier.