https://file.aiquickdraw.com/mathbot/file/1729551468098ajzrh7vm.jpg

The expression shown in the image is:

\[
(\sqrt{-40})(-\sqrt{5})
\]

### Step 1: Simplify the square roots.
- The square root of a negative number involves the imaginary unit \(i\), where \(i = \sqrt{-1}\).
  
\[
\sqrt{-40} = \sqrt{-1 \times 40} = \sqrt{-1} \times \sqrt{40} = i\sqrt{40}
\]
Now, simplify \(\sqrt{40}\):
\[
\sqrt{40} = \sqrt{4 \times 10} = 2\sqrt{10}
\]
So, 
\[
\sqrt{-40} = 2i\sqrt{10}
\]

### Step 2: Multiply the expressions.
Now substitute \(\sqrt{-40}\) and \(\sqrt{5}\) into the original expression:
\[
(2i\sqrt{10})(-\sqrt{5}) = -2i\sqrt{10} \times \sqrt{5}
\]
Now, multiply the square roots:
\[
\sqrt{10} \times \sqrt{5} = \sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}
\]
Thus, the expression becomes:
\[
-2i \times 5\sqrt{2} = -10i\sqrt{2}
\]

### Final Answer:
\[
-10i\sqrt{2}
\]

Let me know if you need further details or have questions.

Here are five related questions you might find helpful:
1. What is the imaginary unit \(i\) and how is it used in complex numbers?
2. How do you simplify square roots of non-perfect squares?
3. How can you express the square root of a negative number?
4. What are the rules for multiplying complex numbers and square roots?
5. How does the distributive property apply when multiplying expressions with imaginary numbers?

**Tip:** When dealing with square roots of negative numbers, always express them in terms of the imaginary unit \(i\), to handle complex numbers properly.

Learn how to multiply complex numbers involving the square roots √-40 and -√5. This detailed step-by-step solution explains key concepts such as imaginary numbers, simplifying radicals, and complex multiplication. Suitable for students in Grades 10-12.

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