https://file.aiquickdraw.com/mathbot/file/17338373777436emfhbkn.jpg

The given expression appears to be a mathematical equation or formula. Let me transcribe and solve it.

The uploaded image appears to show the following mathematical expression:

\[
\sqrt{\frac{\sqrt{x + \sqrt{7}}}{x + \sqrt{7}}}
\]

Let’s simplify and analyze this expression:

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### Simplification:

1. The numerator inside the square root is:
   \[
   \sqrt{x + \sqrt{7}}
   \]

2. The denominator inside the square root is:
   \[
   x + \sqrt{7}
   \]

3. The full expression under the outer square root becomes:
   \[
   \sqrt{\frac{\sqrt{x + \sqrt{7}}}{x + \sqrt{7}}}
   \]

   Since \( x + \sqrt{7} > 0 \) (assuming \( x > -\sqrt{7} \)), we can simplify step by step.

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### Final Simplified Form:
The simplification depends on the specific constraints of \( x \), but the result simplifies as:

\[
\boxed{\sqrt{\frac{1}{\sqrt{x + \sqrt{7}}}}}
\]

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Let me know if you'd like detailed steps or further analysis!

### **Follow-up Questions**
1. Would you like a detailed step-by-step breakdown of the simplification process?
2. Are there any constraints or assumptions for \( x \) you’d like me to consider?
3. Should I rewrite this in a different mathematical context (e.g., logarithms or trigonometric substitution)?
4. Do you need a graph or numerical evaluation of this expression for specific values of \( x \)?
5. Would you like me to explore related expressions (e.g., with cube roots or higher-order roots)?

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### **Tip**  
When working with nested roots, simplify step by step while considering the domain of the variables!

Simplify the expression \( \sqrt{\frac{\sqrt{x + \sqrt{7}}}{x + \sqrt{7}}} \).

Explore the step-by-step simplification of the nested radical expression \( \sqrt{\frac{\sqrt{x + \sqrt{7}}}{x + \sqrt{7}}} \). This problem covers key concepts in simplifying radical expressions and understanding properties of square roots. Suitable for students in Grades 9-11.

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