Write the square root as the product of two square roots. 1-$$ \sqrt{-45} $$

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.

Learn how to express the square root of -45 as the product of two square roots. This detailed solution involves complex numbers, including the imaginary unit i and properties of square roots. Suitable for students in Grades 9-12.

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