The expression you've provided is:

\[
\sqrt{\frac{36}{81}}
\]

First, let's simplify the fraction under the square root:

\[
\frac{36}{81} = \frac{6^2}{9^2} = \left(\frac{6}{9}\right)^2 = \left(\frac{2}{3}\right)^2
\]

Now, taking the square root of the square:

\[
\sqrt{\left(\frac{2}{3}\right)^2} = \frac{2}{3}
\]

So, the simplified expression is:

\[
\sqrt{\frac{36}{81}} = \frac{2}{3}
\]

Would you like more details on this or have any other questions?

Here are 5 related questions:

1. How do you simplify square roots of fractions in general?
2. What are the properties of square roots that apply to fractions?
3. How do you rationalize the denominator of a fraction involving square roots?
4. Can you simplify the square root of a sum or difference of fractions?
5. What are the differences between simplifying a square root of a fraction and a square root of a product?

**Tip:** When simplifying square roots, always check if the expression inside the root can be factored into perfect squares for easier calculation.

Learn how to simplify the square root of the fraction 36 over 81 step-by-step. This problem covers concepts of square roots and fraction simplification. Suitable for students in Grades 7-9.

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