The problem asks you to identify which point on the number line most closely represents $\sqrt{97}$.

Let's start by approximating $\sqrt{97}$.

We know that:

• $\sqrt{100} = 10$
• $\sqrt{81} = 9$

Since $97$ is closer to $100$ than it is to $81$, we can conclude that $\sqrt{97}$ is slightly less than $10$.

By calculating $\sqrt{97}$ approximately, we get:

$\sqrt{97} \approx 9.848$

This means $\sqrt{97}$ is approximately 9.848, which is just slightly less than 9.9. Looking at the number line, the point labeled "e" is closest to 9.848.

Therefore, the correct answer is B) e.

Would you like a further explanation or have any questions about this process?

Here are some related questions to deepen your understanding:

1. How can you estimate square roots of numbers that are not perfect squares?
2. What is the difference between estimating square roots and using a calculator for exact values?
3. How can you use a number line to represent square roots more accurately?
4. What are some methods for approximating square roots without a calculator?
5. How would you handle estimating higher square roots, like $\sqrt{105}$?

Tip: If you need a quick approximation for square roots of numbers between two perfect squares, you can use the average of the two square roots as a rough estimate.