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Find the square
roots then plot the
given irrational
numbers on the
number line.

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**.

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

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### 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 \( 9 \).

Find the square roots then plot the given irrational numbers on the number line.

Learn how to find the square roots of irrational numbers like √78, √34, √75, √95, and √8 and plot them accurately on a number line. This lesson helps students in Grades 7-10 understand how to approximate square roots and visually represent them.

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