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

Certainly! Let's determine between which consecutive integers each of the given numbers lies. 1. **\( \sqrt{5} \)** - Calculate squares of integers around \( \sqrt{5} \): - \( 2^2 = 4 \) - \( 3^2 = 9 \) - Since \( 4 < 5 < 9 \), - **\( \sqrt{5} \) lies between **2 and 3**. 2. **\( \sqrt[3]{42} \)** - Calculate cubes of integers around \( \sqrt[3]{42} \): - \( 3^3 = 27 \) - \( 4^3 = 64 \) - Since \( 27 < 42 < 64 \), - **\( \sqrt[3]{42} \) lies between **3 and 4**. 3. **\( -\sqrt{12} \)** - First, find \( \sqrt{12} \): - \( \sqrt{12} \approx 3.464 \) - So, \( -\sqrt{12} \approx -3.464 \) - It lies between: - \( -4 \) and \( -3 \) - **\( -\sqrt{12} \) lies between **-4 and -3**. 4. **\( -\sqrt{71} \)** - First, find \( \sqrt{71} \): - \( \sqrt{71} \approx 8.426 \) - So, \( -\sqrt{71} \approx -8.426 \) - It lies between: - \( -9 \) and \( -8 \) - **\( -\sqrt{71} \) lies between **-9 and -8**. 5. **\( \sqrt{11} \)** - Calculate squares of integers around \( \sqrt{11} \): - \( 3^2 = 9 \) - \( 4^2 = 16 \) - Since \( 9 < 11 < 16 \), - **\( \sqrt{11} \) lies between **3 and 4**. --- **Summary:** 1. \( \sqrt{5} \) is between **2 and 3**. 2. \( \sqrt[3]{42} \) is between **3 and 4**. 3. \( -\sqrt{12} \) is between **-4 and -3**. 4. \( -\sqrt{71} \) is between **-9 and -8**. 5. \( \sqrt{11} \) is between **3 and 4**.