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.