Question

Place the numbers to the best spot possible on the number line. Click Here for Help VideoUndoRedoDRAG DROP VALUES135\sqrt{35}35​273\sqrt{73}73​352\frac{5}{2}25​420\sqrt{20}20​519681\sqrt{\frac{196}{81}}81196​​

Answer 1

To place the numbers on a number line, we first need to evaluate or approximate each value. Here's a breakdown of the given numbers:

1. **135**: This is simply 135.

2. **\(\sqrt{35}\)**:
- \(\sqrt{35} \approx 5.92\) (since \(5.92^2 \approx 35\))

3. **35**: This is simply 35.

4. **273**: This is simply 273.

5. **\(\frac{5}{2}\)**:
- \(\frac{5}{2} = 2.5\)

6. **\(\sqrt{20}\)**:
- \(\sqrt{20} \approx 4.47\) (since \(4.47^2 \approx 20\))

7. **19**: This is simply 19.

8. **\(\sqrt{\frac{196}{81}}\)**:
- \(\sqrt{\frac{196}{81}} = \frac{\sqrt{196}}{\sqrt{81}} = \frac{14}{9} \approx 1.56\)

9. **81**: This is simply 81.

10. **196**: This is simply 196.

Now we can approximate all the numbers:

- \(\frac{5}{2} \approx 2.5\)
- \(\sqrt{35} \approx 5.92\)
- \(\sqrt{20} \approx 4.47\)
- \(\sqrt{\frac{196}{81}} \approx 1.56\)
- 19
- 35
- 81
- 135
- 196
- 273

Next, we sort these values:

- \(\sqrt{\frac{196}{81}} \approx 1.56\)
- \(\frac{5}{2} = 2.5\)
- \(\sqrt{20} \approx 4.47\)
- \(\sqrt{35} \approx 5.92\)
- 19
- 35
- 81
- 135
- 196
- 273

Placed on the number line, we would have:

1. **\(\sqrt{\frac{196}{81}} \approx 1.56\)**
2. **\(\frac{5}{2} = 2.5\)**
3. **\(\sqrt{20} \approx 4.47\)**
4. **\(\sqrt{35} \approx 5.92\)**
5. **19**
6. **35**
7. **81**
8. **135**
9. **196**
10. **273**

Make sure to represent this accurately when placing on your number line! If you need help visualizing or positioning, please let me know!

Answer 2

What about
1
73\sqrt{73}
73

Answer 3

To place the numbers \(1\), \(\sqrt{73}\), and \(73\) on a number line, we first need to evaluate or approximate the square root of \(73\).

1. **1**: This is simply \(1\).

2. **\(\sqrt{73}\)**:
- \(\sqrt{73} \approx 8.54\) (since \(8.54^2 \approx 73\))

3. **73**: This is simply \(73\).

Now we can arrange the three numbers in order:

- \(1\)
- \(\sqrt{73} \approx 8.54\)
- \(73\)

Thus, if you were to place them on a number line, they would be positioned approximately as follows:

1. **1**
2. **\(\sqrt{73} \approx 8.54\)**
3. **73**

Make sure to accurately represent their positions based on their numerical values when marking on the number line! If you need further assistance, feel free to ask.