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The expression you're asked to simplify is \( 9 \sqrt{117} \).

To simplify this expression, we first check if \( \sqrt{117} \) can be simplified by factoring the number 117:

\[ 117 = 3^2 \times 13 \]

Since 117 can be factored into \( 3^2 \times 13 \), we can simplify the square root:

\[
\sqrt{117} = \sqrt{3^2 \times 13} = 3\sqrt{13}
\]

Now, multiply this result by 9:

\[
9 \sqrt{117} = 9 \times 3 \sqrt{13} = 27 \sqrt{13}
\]

Thus, the simplified form of \( 9 \sqrt{117} \) is:

\[
27 \sqrt{13}
\]

Would you like more details or have any questions?

Here are five questions for further exploration:
1. How would you simplify \( \sqrt{180} \)?
2. What are the steps to simplify \( \sqrt{200} \)?
3. Can all square roots of numbers be simplified? Why or why not?
4. How does the property \( \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} \) help in simplifying square roots?
5. What is the simplified form of \( 5 \sqrt{72} \)?

**Tip:** Always try to break down the radicand (the number inside the square root) into prime factors to simplify square roots efficiently.

Learn how to simplify the radical expression 9√117 step-by-step. This solution involves factoring and applying the product property of square roots. Suitable for students in Grades 7-9.

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