Explanation:

Correct option 1: 4√13

To determine which of the numbers √5, 3√7, and 4√13 is the largest, we can compare their squares to avoid dealing with square roots directly.

1. Calculate the square of each number:
- For √5:
(√5⁾²=5
- For 3√7:
(3√7)²=3²⋅(√7)²=9⋅7=63
- For 4√13:
(4√13)²=4²⋅(√13)²=16⋅13=208

2. Compare the squared values:
- We have:
- √5²=5
- 3√7²=63
- 4√13²=208

3. Identify the largest squared value:
- Comparing the results:
- 5<63<208

4. Conclusion:
- Since 208 is the largest squared value, it follows that 4√13 is the largest among the three numbers.

Final Answer:
The largest number among √5, 3√7, and 4√13 is 4√13.