To solve the problem:

Step 1: Calculate $7\sqrt{2}$

• Approximate $\sqrt{2} \approx 1.414$, so: $7\sqrt{2} \approx 7 \times 1.414 = 9.898$

Step 2: Calculate $3\pi$

• Approximate $\pi \approx 3.1416$, so: $3\pi \approx 3 \times 3.1416 = 9.425$

Step 3: Plot on the number line

• $7\sqrt{2}$ is approximately $9.898$, which is close to 9.9.
• $3\pi$ is approximately $9.425$, which is between 9.4 and 9.5.

Step 4: Compare $7\sqrt{2}$ and $3\pi$

• Clearly, $7\sqrt{2} > 3\pi$.

Would you like further details or explanations? Here are some related questions for you:

1. How do you calculate square roots manually or using a calculator?
2. Why is $\pi$ an irrational number, and what does it mean?
3. Can we estimate $\sqrt{2}$ more precisely for higher accuracy?
4. What real-life applications involve comparing such irrational numbers?
5. How can a number line help visualize such comparisons?

Tip: Always double-check calculations when dealing with approximations of irrational numbers.