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To compare \(\sqrt{2}\) and 3.1, let's first calculate the value of \(\sqrt{2}\) to determine which number is larger.

- The value of \(\sqrt{2} \approx 1.414\).

Now comparing 1.414 and 3.1:
- \(1.414 < 3.1\).

So, the correct comparison symbol would be \( \sqrt{2} < 3.1 \).

Would you like any further details or have any questions about this comparison?

Here are five related questions for further exploration:
1. What is the value of \(\sqrt{3}\) compared to 3.1?
2. How can you approximate other square roots without a calculator?
3. What are the real-world applications of comparing square roots and whole numbers?
4. How do you determine whether a square root is rational or irrational?
5. How does \(\sqrt{2}\) compare to 2.5?

**Tip:** When estimating square roots, knowing the approximate values of common roots like \(\sqrt{2}\), \(\sqrt{3}\), and \(\sqrt{5}\) can help quickly compare them to other numbers.

Learn how to compare the square root of 2 (\(\sqrt{2}\)) and 3.1 by calculating the value of \(\sqrt{2}\), approximately 1.414, and comparing it to 3.1. This problem highlights the concept of square roots and number comparisons. Suitable for Grades 6-8.

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