The problem asks to round the cube root of 15 to the nearest tenth using a number line. Let's go through the steps:

Step 1: Approximate the Cube Root of 15

We know that: $\sqrt[3]{15}$ To estimate this, notice that: [ \sqrt[3]{8} = 2 \quad \text{and} \quad \sqrt[3]{27} = 3 ] Since 15 is between 8 and 27, the cube root of 15 must be between 2 and 3. Using a calculator, we find: $\sqrt[3]{15} \approx 2.466$

Step 2: Round to the Nearest Tenth

Rounding 2.466 to the nearest tenth gives 2.5.

If using a number line, we could place 2.466 between 2.4 and 2.5. Since it's closer to 2.5, we round up.

Final Answer:

The cube root of 15 rounded to the nearest tenth is 2.5.

Would you like further details or any clarifications? Here are some additional questions to expand this topic:

1. What is the cube root of other numbers between 15 and 27?
2. Can you explain how to estimate cube roots without a calculator?
3. How would you plot cube roots of different numbers on a number line?
4. What is the difference between square roots and cube roots?
5. How do you round numbers to other decimal places, such as hundredths?

Tip: When estimating roots, try to first find two perfect cubes or squares between which the number lies.