Determine between which intey the following numbers lies: 1) $$ \sqrt{5} $$ 2) $$ \sqrt[3]{42} $$ 3) $$ -\sqrt{12} $$ 4) $$ -\sqrt{71} $$ 5) $$ \sqrt{11} $$

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Certainly! Let's determine between which **integers** each of the given numbers lies.

### 1) $$ \sqrt{5} $$

- **Calculation:**
  - $$ 2^2 = 4 $$
  - $$ 3^2 = 9 $$
- **Conclusion:** $$ 4 < 5 < 9 $$ implies $$ 2 < \sqrt{5} < 3 $$.

### 2) $$ \sqrt[3]{42} $$

- **Calculation:**
  - $$ 3^3 = 27 $$
  - $$ 4^3 = 64 $$
- **Conclusion:** $$ 27 < 42 < 64 $$ implies $$ 3 < \sqrt[3]{42} < 4 $$.

### 3) $$ -\sqrt{12} $$

- **Calculation:**
  - $$ \sqrt{12} \approx 3.464 $$
  - Thus, $$ -\sqrt{12} \approx -3.464 $$
- **Conclusion:** $$ -4 < -3.464 < -3 $$ implies $$ -4 < -\sqrt{12} < -3 $$.

### 4) $$ -\sqrt{71} $$

- **Calculation:**
  - $$ \sqrt{71} \approx 8.426 $$
  - Thus, $$ -\sqrt{71} \approx -8.426 $$
- **Conclusion:** $$ -9 < -8.426 < -8 $$ implies $$ -9 < -\sqrt{71} < -8 $$.

### 5) $$ \sqrt{11} $$

- **Calculation:**
  - $$ 3^2 = 9 $$
  - $$ 4^2 = 16 $$
- **Conclusion:** $$ 9 < 11 < 16 $$ implies $$ 3 < \sqrt{11} < 4 $$.

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**Summary of Results:**

1. $$ 2 < \sqrt{5} < 3 $$
2. $$ 3 < \sqrt[3]{42} < 4 $$
3. $$ -4 < -\sqrt{12} < -3 $$
4. $$ -9 < -\sqrt{71} < -8 $$
5. $$ 3 < \sqrt{11} < 4 $$
$$ \sqrt{5} $$ is between 2 and 3, $$ \sqrt[3]{42} $$ is between 3 and 4, $$ -\sqrt{12} $$ is between -4 and -3, $$ -\sqrt{71} $$ is between -9 and -8, and $$ \sqrt{11} $$ is between 3 and 4.

Determine between which intey the following numbers lies: 1) \( \sqrt{5} \) 2) \( \sqrt[3]{42} \) 3) \( -\sqrt{12} \) 4) \( -\sqrt{71} \) 5) \( \sqrt{11} \)

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