https://file.aiquickdraw.com/mathbot/file/17279212307469mr61w69.jpg

In this image, you're tasked with plotting \( \sqrt{68} \) on the number line as accurately as possible.

To solve this:

1. First, calculate \( \sqrt{68} \). Using a calculator or approximating, we find:
   \[
   \sqrt{68} \approx 8.246
   \]

2. On the given number line, the value of \( \sqrt{68} \) (which is approximately 8.246) lies between 8 and 9, closer to 8 but slightly past the midpoint. 

3. Since \( \sqrt{68} \approx 8.246 \), this means it is a little past 8.2. So, the correct place to plot it would be just after 8.2 on the number line, as shown by the red indicator in your diagram, which seems reasonably placed.

Would you like more details or further explanation?

### Related Questions:
1. How do you calculate the square root of non-perfect squares?
2. Why does \( \sqrt{68} \) lie between 8 and 9?
3. How can we approximate square roots more precisely?
4. What is the difference between estimating \( \sqrt{68} \) and finding its exact value?
5. Can you plot other square roots like \( \sqrt{72} \) or \( \sqrt{50} \) on the same number line?

### Tip:
When estimating square roots, it's helpful to know the squares of nearby whole numbers for quicker approximations. For example, \( 8^2 = 64 \) and \( 9^2 = 81 \), so \( \sqrt{68} \) should lie between 8 and 9.

Plot √68 on the decimal number line as accurately as possible.

Learn how to accurately plot √68, approximately 8.246, on a decimal number line. This step-by-step solution guides you through calculating the square root and placing it between 8 and 9, slightly past 8.2.

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