https://file.aiquickdraw.com/mathbot/file/17266903320865ilpngea.jpg

Let's solve the problem step-by-step.

Given:
- The first expression is \(8\sqrt{2}\)
- The second expression is \(5\sqrt{10}\)

We need to find the product of these two expressions in simplest radical form.

### Step 1: Multiply the coefficients (numbers outside the radicals)
\[
8 \times 5 = 40
\]

### Step 2: Multiply the radicals (numbers inside the square root)
\[
\sqrt{2} \times \sqrt{10} = \sqrt{2 \times 10} = \sqrt{20}
\]

### Step 3: Combine the results
\[
40 \sqrt{20}
\]

### Step 4: Simplify the square root if possible
\[
\sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2\sqrt{5}
\]

### Step 5: Substitute back to get the simplest form
\[
40 \times 2\sqrt{5} = 80\sqrt{5}
\]

So, the product of \(8\sqrt{2}\) and \(5\sqrt{10}\) in simplest radical form is \( \mathbf{80\sqrt{5}} \).

Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. What is the product of \(3\sqrt{3}\) and \(4\sqrt{6}\) in simplest radical form?
2. How do you simplify \( \sqrt{50} \)?
3. What is the product of \(7\sqrt{5}\) and \(2\sqrt{3}\)?
4. How can you simplify \(12\sqrt{8}\) into its simplest form?
5. What is the sum of \(4\sqrt{3}\) and \(6\sqrt{3}\)?

**Tip:** Remember that when multiplying radicals, you can combine them under a single square root if they have the same index.

What is the product of 8√2 and 5√10 in simplest radical form?

Learn how to calculate the product of 8√2 and 5√10 in simplest radical form. This problem involves multiplying radicals and simplifying square roots, suitable for students in Grades 8-10.

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