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Let's solve the problem by finding the product of \( 9 \) and \( 8\sqrt{90} \), and simplifying the radical.

### Step 1: Multiply the constants
We multiply the constants \( 9 \) and \( 8 \):
\[
9 \times 8 = 72
\]

### Step 2: Simplify \( \sqrt{90} \)
To simplify \( \sqrt{90} \), we break it down into prime factors:
\[
\sqrt{90} = \sqrt{9 \times 10} = \sqrt{9} \times \sqrt{10}
\]
Since \( \sqrt{9} = 3 \), we get:
\[
\sqrt{90} = 3\sqrt{10}
\]

### Step 3: Multiply the simplified terms
Now, we multiply \( 72 \) by \( 3\sqrt{10} \):
\[
72 \times 3\sqrt{10} = 216\sqrt{10}
\]

### Final Answer:
The product of \( 9 \) and \( 8\sqrt{90} \) in simplest radical form is:
\[
216\sqrt{10}
\]

Would you like more details or have any questions about the solution?

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Here are 5 related questions to explore:
1. What is the product of \( 7 \) and \( 5\sqrt{50} \) in simplest radical form?
2. How do you simplify \( \sqrt{72} \)?
3. What are the prime factors of 90?
4. How would you express the product of \( 4 \) and \( 6\sqrt{45} \)?
5. What is the square root of 144?

**Tip:** When simplifying radicals, always look for perfect squares within the number to simplify it easily!

What is the product of 9 and 8√90 in simplest radical form?

Learn how to find the product of 9 and 8√90 in its simplest radical form. This problem involves multiplying constants, simplifying square roots, and basic algebraic techniques, suitable for Grades 8-10.

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