Simplify the expression. 
RootIndex 4 StartRoot StartFraction 6 Over 25 EndFraction EndRoot

The expression you're looking to simplify is:

\[
\sqrt[4]{\frac{6}{25}}
\]

To simplify this, we can separate the numerator and the denominator under the fourth root:

\[
\sqrt[4]{\frac{6}{25}} = \frac{\sqrt[4]{6}}{\sqrt[4]{25}}
\]

Since \( 25 = 5^2 \), we can simplify \( \sqrt[4]{25} \):

\[
\sqrt[4]{25} = \sqrt[4]{5^2} = 5^{\frac{2}{4}} = 5^{\frac{1}{2}} = \sqrt{5}
\]

Thus, the simplified expression becomes:

\[
\frac{\sqrt[4]{6}}{\sqrt{5}}
\]

This is the simplified form of the given expression.

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you simplify fractional exponents?
2. How would you solve \( \sqrt[4]{\frac{16}{81}} \)?
3. What is the difference between square roots and fourth roots?
4. Can irrational numbers be simplified further?
5. How do you estimate \( \sqrt[4]{6} \) without a calculator?

**Tip**: Whenever simplifying roots, always check if the terms inside the root can be factored into perfect powers.

Simplify the expression. RootIndex 4 StartRoot StartFraction 6 Over 25 EndFraction EndRoot

Learn how to simplify the expression involving the fourth root of a fraction: \( \sqrt[4]{\frac{6}{25}} \). This problem covers key concepts like radical simplification and fractional exponents, suitable for students in Grades 9-11.

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