The given expression is:

\[
\frac{\sqrt{59.29} - \sqrt{5.29}}{\sqrt{59.29} + \sqrt{5.29}}
\]

Let's simplify this expression step by step.

1. **Approximate square roots:**
   - \(\sqrt{59.29} \approx 7.7\)
   - \(\sqrt{5.29} \approx 2.3\)

2. **Substitute these values into the expression:**
   \[
   \frac{7.7 - 2.3}{7.7 + 2.3} = \frac{5.4}{10} = 0.54
   \]

Thus, the simplified value of the given expression is approximately \(0.54\).

Would you like more details, or do you have any other questions?

Here are 5 related questions to explore further:
1. How do you simplify an expression involving square roots in general?
2. How does rationalizing the denominator work?
3. What is the binomial conjugate, and how is it useful in simplifying square root expressions?
4. How do approximation methods affect the precision of a solution?
5. How do square root operations impact the behavior of functions?

**Tip:** Rationalizing expressions like these can sometimes lead to simpler forms, especially when dealing with radicals.

Learn how to simplify the radical expression √59.29−√5.29/√59.29+√5.29 with a step-by-step solution. This problem covers key algebraic concepts, including the rationalization of denominators and properties of square roots. Suitable for students in Grades 9-11.

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