Write in ascending order:
`6 sqrt(5) , 7 sqrt(3)` and `8 sqrt(2)`

Answer

To write the numbers \(6 \sqrt{5}\), \(7 \sqrt{3}\), and \(8 \sqrt{2}\) in ascending order, we can follow these steps:

### Step 1: Calculate the approximate decimal values of each expression.

1. **Calculate \(6 \sqrt{5}\)**:
- The approximate value of \(\sqrt{5} \approx 2.236\).
- Therefore, \(6 \sqrt{5} \approx 6 \times 2.236 \approx 13.416\).

2. **Calculate \(7 \sqrt{3}\)**:
- The approximate value of \(\sqrt{3} \approx 1.732\).
- Therefore, \(7 \sqrt{3} \approx 7 \times 1.732 \approx 12.124\).

3. **Calculate \(8 \sqrt{2}\)**:
- The approximate value of \(\sqrt{2} \approx 1.414\).
- Therefore, \(8 \sqrt{2} \approx 8 \times 1.414 \approx 11.312\).

### Step 2: Compare the calculated values.

- \(6 \sqrt{5} \approx 13.416\)
- \(7 \sqrt{3} \approx 12.124\)
- \(8 \sqrt{2} \approx 11.312\)

### Step 3: Arrange the values in ascending order.

From the calculated values:
- \(8 \sqrt{2} \approx 11.312\) (smallest)
- \(7 \sqrt{3} \approx 12.124\) (middle)
- \(6 \sqrt{5} \approx 13.416\) (largest)

### Final Answer:
The numbers in ascending order are:
\[ 8 \sqrt{2}, 7 \sqrt{3}, 6 \sqrt{5} \]

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