To determine which point best represents $\sqrt{10}$ on the number line, let's follow these steps:

1. Find an approximate value of $\sqrt{10}$: $\sqrt{10} \approx 3.162$

2. Compare this value with the points on the number line:

   • Point $A$: Corresponds to 2.
   • Point $B$: Corresponds to 3.
   • Point $C$: Corresponds to 4.
   • Point $D$: Corresponds to 10.

   Since $\sqrt{10} \approx 3.162$, it lies between 3 and 4 but closer to 3.

3. Select the closest point: Based on the number line provided, the point closest to $\sqrt{10}$ is point B.

Correct answer: B. point B

Would you like a detailed explanation of how square roots are approximated or visualized?

Related Questions:

1. What is the definition of a square root, and why does $\sqrt{10}$ fall between 3 and 4?
2. How can you approximate square roots without a calculator?
3. Why is the placement of square roots on a number line important in understanding numbers?
4. How do irrational numbers like $\sqrt{10}$ differ from integers on a number line?
5. Can $\sqrt{10}$ be expressed as a fraction?

Tip:

To estimate square roots of non-perfect squares, identify the two closest perfect squares (e.g., for $10$, use $9 = 3^2$ and $16 = 4^2$), then refine the estimate!