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The given problem asks which sign (either \(>\) or \(<\)) makes the statement true for:

\[
\sqrt{10} \, ? \, 2 \frac{1}{2}
\]

### Step-by-step solution:

1. **Evaluate \(\sqrt{10}\):**
   \[
   \sqrt{10} \approx 3.162
   \]

2. **Convert \(2 \frac{1}{2}\) to an improper fraction or decimal:**
   \[
   2 \frac{1}{2} = 2 + \frac{1}{2} = 2.5
   \]

3. **Compare the two values:**
   - \(\sqrt{10} \approx 3.162\)
   - \(2 \frac{1}{2} = 2.5\)

Since \(3.162 > 2.5\), the correct sign is:

\[
\sqrt{10} > 2 \frac{1}{2}
\]

Therefore, the correct symbol to make the statement true is **greater than (\(>\))**.

Would you like more details or further clarifications?

### Related questions:
1. How is the square root of a number calculated?
2. What are other ways to compare irrational numbers and mixed numbers?
3. How can mixed fractions be converted into improper fractions?
4. What other properties of square roots can help in comparing values?
5. How does one calculate square roots without a calculator?

### Tip:
When comparing numbers, converting them into decimals can often make comparisons easier, especially when dealing with square roots or mixed numbers.

Which sign makes the statement true? √10 ? 2 1/2

Learn how to determine which inequality sign makes the statement √10 ? 2 1/2 true. This math problem involves concepts like square roots, converting mixed numbers to decimals, and comparing irrational and rational numbers. Suitable for students in Grades 6-8.

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