Here is the image showing the representation of $\sqrt{10}$ and $\sqrt{4.5}$ on the number line. Let me know if you have any questions or need further explanation!

Follow-up Questions:

1. How do you determine the exact location of a square root on a number line?
2. Can this method be used for non-square roots like cube roots?
3. What is the importance of using a midpoint in this construction method?
4. How would you represent $\sqrt{2}$ on the number line?
5. Why is the perpendicular line important in this geometric construction?

Tip:

Geometric constructions on a number line are a visual and intuitive way to understand square roots, especially when dealing with irrational numbers that cannot be easily placed on the number line using simple fractions.