Let's calculate the square roots of the given numbers and determine approximately where they should be placed on the number lines:

1. $\sqrt{78}$

• $\sqrt{78} \approx 8.83$
• This will be slightly before 9 on the number line.

2. $\sqrt{34}$

• $\sqrt{34} \approx 5.83$
• This falls slightly before 6.

3. $\sqrt{75}$

• $\sqrt{75} \approx 8.66$
• This is also just before 9.

4. $\sqrt{95}$

• $\sqrt{95} \approx 9.75$
• This will be very close to 10.

5. $\sqrt{8}$

• $\sqrt{8} \approx 2.83$
• This is placed just before 3.

Now, place these points appropriately on the number lines.

1. For $\sqrt{78}$, mark around 8.8.
2. For $\sqrt{34}$, mark around 5.8.
3. For $\sqrt{75}$, mark around 8.7.
4. For $\sqrt{95}$, mark around 9.8.
5. For $\sqrt{8}$, mark around 2.8.

Would you like more detailed guidance on how to plot these values accurately?

5 Related Questions:

1. What is the difference between rational and irrational numbers?
2. How do you estimate square roots of non-perfect squares?
3. How do calculators compute square roots internally?
4. How do you represent irrational numbers on a number line in general?
5. What are the properties of square roots?

Tip: Always check between which two perfect squares a number lies when estimating square roots. For example, $78$ lies between $64$ and $81$, giving us a rough idea that $\sqrt{78}$ will be between $8$ and $9$.