Estimate the following square root solutions. \begin{tabular}{lll} 33. Is $$ \sqrt{5} $$ closer to 2 or $$ 3 ? $$ & 37. Is $$ \sqrt{79} $$ closer to 8 or $$ 9 ? $$ \ 34. Is $$ \sqrt{52} $$ closer to 7 or $$ 8 ? $$ & 38. Is $$ \sqrt{106} $$ closer to 10 or $$ 11 ? $$ \ 35. Is $$ \sqrt{130} $$ closer to 11 or $$ 12 ? $$ & 39. Is $$ \sqrt{160} $$ closer to 12 or $$ 13 ? $$ \ 36. Is $$ \sqrt{619} $$ closer to 24 or $$ 25 ? $$ & 40. Is $$ \sqrt{29} $$ closer to 5 or $$ 6 ? $$ \ \hline\end{tabular}

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**33. Is $$ \sqrt{5} $$ closer to 2 or 3?**

- Notice that $$2^2 = 4$$ and $$3^2 = 9$$. Thus, $$ \sqrt{5} $$ lies between 2 and 3.
- A rough estimate: $$ \sqrt{5} \approx 2.236 $$.
- Distance from 2: $$ 2.236 - 2 = 0.236 $$.  
  Distance from 3: $$ 3 - 2.236 = 0.764 $$.
- Hence, $$ \sqrt{5} $$ is closer to **2**.

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**34. Is $$ \sqrt{52} $$ closer to 7 or 8?**

- Notice that $$7^2 = 49$$ and $$8^2 = 64$$. So, $$ \sqrt{52} $$ lies between 7 and 8.
- A rough estimate: $$ \sqrt{52} \approx 7.211 $$.
- Distance from 7: $$ 7.211 - 7 = 0.211 $$.  
  Distance from 8: $$ 8 - 7.211 = 0.789 $$.
- Hence, $$ \sqrt{52} $$ is closer to **7**.

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**35. Is $$ \sqrt{130} $$ closer to 11 or 12?**

- Notice that $$11^2 = 121$$ and $$12^2 = 144$$. So, $$ \sqrt{130} $$ lies between 11 and 12.
- A rough estimate: $$ \sqrt{130} \approx 11.4 $$.
- Distance from 11: $$ 11.4 - 11 = 0.4 $$.  
  Distance from 12: $$ 12 - 11.4 = 0.6 $$.
- Hence, $$ \sqrt{130} $$ is closer to **11**.

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**36. Is $$ \sqrt{619} $$ closer to 24 or 25?**

- Notice that $$24^2 = 576$$ and $$25^2 = 625$$. So, $$ \sqrt{619} $$ lies between 24 and 25.
- Compute distances:  
  $$619 - 576 = 43$$ and $$625 - 619 = 6$$.
- The value is much nearer to 625.
- Hence, $$ \sqrt{619} $$ is closer to **25**.

---

**37. Is $$ \sqrt{79} $$ closer to 8 or 9?**

- Notice that $$8^2 = 64$$ and $$9^2 = 81$$. So, $$ \sqrt{79} $$ lies between 8 and 9.
- A rough estimate: $$ \sqrt{79} \approx 8.888 $$.
- Distance from 8: $$ 8.888 - 8 \approx 0.888 $$.  
  Distance from 9: $$ 9 - 8.888 \approx 0.112 $$.
- Hence, $$ \sqrt{79} $$ is closer to **9**.

---

**38. Is $$ \sqrt{106} $$ closer to 10 or 11?**

- Notice that $$10^2 = 100$$ and $$11^2 = 121$$. So, $$ \sqrt{106} $$ lies between 10 and 11.
- A rough estimate: $$ \sqrt{106} \approx 10.295 $$.
- Distance from 10: $$ 10.295 - 10 = 0.295 $$.  
  Distance from 11: $$ 11 - 10.295 = 0.705 $$.
- Hence, $$ \sqrt{106} $$ is closer to **10**.

---

**39. Is $$ \sqrt{160} $$ closer to 12 or 13?**

- Notice that $$12^2 = 144$$ and $$13^2 = 169$$. So, $$ \sqrt{160} $$ lies between 12 and 13.
- A rough estimate: $$ \sqrt{160} \approx 12.649 $$.
- Distance from 12: $$ 12.649 - 12 \approx 0.649 $$.  
  Distance from 13: $$ 13 - 12.649 \approx 0.351 $$.
- Hence, $$ \sqrt{160} $$ is closer to **13**.

---

**40. Is $$ \sqrt{29} $$ closer to 5 or 6?**

- Notice that $$5^2 = 25$$ and $$6^2 = 36$$. So, $$ \sqrt{29} $$ lies between 5 and 6.
- A rough estimate: $$ \sqrt{29} \approx 5.385 $$.
- Distance from 5: $$ 5.385 - 5 = 0.385 $$.  
  Distance from 6: $$ 6 - 5.385 = 0.615 $$.
- Hence, $$ \sqrt{29} $$ is closer to **5**.
**33. $$ \sqrt{5} $$ is closer to 2.** **34. $$ \sqrt{52} $$ is closer to 7.** **35. $$ \sqrt{130} $$ is closer to 11.** **36. $$ \sqrt{619} $$ is closer to 25.** **37. $$ \sqrt{79} $$ is closer to 9.** **38. $$ \sqrt{106} $$ is closer to 10.** **39. $$ \sqrt{160} $$ is closer to 13.** **40. $$ \sqrt{29} $$ is closer to 5.**

33. Is closer to 2 or	37. Is closer to 8 or
34. Is closer to 7 or	38. Is closer to 10 or
35. Is closer to 11 or	39. Is closer to 12 or
36. Is closer to 24 or	40. Is closer to 5 or

Estimate the following square root solutions.

33. Is closer to 2 or 37. Is closer to 8 or

34. Is closer to 7 or 38. Is closer to 10 or

35. Is closer to 11 or 39. Is closer to 12 or

36. Is closer to 24 or 40. Is closer to 5 or

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Estimate the following square root solutions. 33. Is closer to 2 or 37. Is closer to 8 or 34. Is closer to 7 or 38. Is closer to 10 or 35. Is closer to 11 or 39. Is closer to 12 or 36. Is closer to 24 or 40. Is closer to 5 or