The image contains a list of square roots to be estimated to the nearest integer. I'll go through each one and provide the rounded values:

1. $\sqrt{5} \approx 2.236$ → 2
2. $\sqrt{18} \approx 4.243$ → 4
3. $\sqrt{10} \approx 3.162$ → 3
4. $\sqrt{34} \approx 5.831$ → 6
5. $\sqrt{53} \approx 7.280$ → 7
6. $\sqrt{80} \approx 8.944$ → 9
7. $\sqrt{510} \approx 22.583$ → 23
8. $\sqrt{999} \approx 31.606$ → 32
9. $\sqrt{119} \approx 10.908$ → 11
10. $\sqrt{77} \approx 8.775$ → 9
11. $\sqrt{171} \approx 13.076$ → 13
12. $\sqrt{230} \approx 15.165$ → 15
13. $\sqrt{147} \approx 12.124$ → 12
14. $\sqrt{194} \approx 13.928$ → 14
15. $\sqrt{290\frac{3}{7}} \approx 17.038$ → 17
16. $\sqrt{440} \approx 20.976$ → 21
17. $\sqrt{578} \approx 24.041$ → 24
18. $\sqrt{730} \approx 27.018$ → 27
19. $\sqrt{780} \approx 27.928$ → 28
20. $\sqrt{1,370} \approx 37.011$ → 37
21. $\sqrt{947} \approx 30.774$ → 31
22. $\sqrt{17.8} \approx 4.216$ → 4
23. $\sqrt{11.5} \approx 3.391$ → 3
24. $\sqrt{37.7} \approx 6.139$ → 6
25. $\sqrt{23.8} \approx 4.878$ → 5
26. $\sqrt{59.4} \approx 7.709$ → 8
27. $\sqrt{97.3} \approx 9.862$ → 10
28. $\sqrt{32.5} \approx 5.701$ → 6
29. $\sqrt{211.7} \approx 14.551$ → 15
30. $\sqrt{692.9} \approx 26.324$ → 26

Let me know if you want more details or explanations for any of the steps!

Here are five questions you might explore:

1. What is the method to approximate square roots manually?
2. How can you quickly estimate square roots without a calculator?
3. Why is the square root of a non-perfect square irrational?
4. What is the significance of the square root function in real-life applications?
5. How can the precision of square root estimations affect real-world measurements?

Tip: Memorizing the square roots of perfect squares up to at least 20 can help estimate values faster!