Simplify.  Assume that all variables represent nonnegative real numbers.
StartRoot StartFraction y Superscript 4 Over 81 EndFraction EndRoot

We are asked to simplify the expression:

\[
\sqrt{\frac{y^4}{81}}
\]

### Step-by-Step Solution:

1. **Use the property of square roots**:  
   We can rewrite the square root of a fraction as the square root of the numerator divided by the square root of the denominator:
   \[
   \sqrt{\frac{y^4}{81}} = \frac{\sqrt{y^4}}{\sqrt{81}}
   \]

2. **Simplify the square roots**:  
   - The square root of \( y^4 \) is \( y^2 \) because:
     \[
     \sqrt{y^4} = y^{4/2} = y^2
     \]
   - The square root of 81 is 9 because:
     \[
     \sqrt{81} = 9
     \]

3. **Write the simplified result**:
   \[
   \frac{\sqrt{y^4}}{\sqrt{81}} = \frac{y^2}{9}
   \]

Thus, the simplified expression is:

\[
\frac{y^2}{9}
\]

Let me know if you'd like further details!

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Here are 5 related questions:
1. How do you simplify \(\sqrt{\frac{x^6}{16}}\)?
2. What is the square root of \(\frac{y^2}{25}\)?
3. How do you simplify \(\sqrt{a^8}\)?
4. Can you explain the properties of exponents when simplifying radicals?
5. What happens if the variables are not nonnegative?

**Tip**: When simplifying expressions with square roots, always check if the expression can be factored to help with simplification.

Simplify. Assume that all variables represent nonnegative real numbers. StartRoot StartFraction y Superscript 4 Over 81 EndFraction EndRoot

Simplify the radical expression √(y^4 / 81) step-by-step by applying square root properties. This problem involves key concepts such as radicals, exponents, and properties of square roots, making it suitable for students in Grades 8-10.

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