1. **Problem 1a:** Solve $\sqrt{49} \times \sqrt{49}$. - We use the property $\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$. - So, $\sqrt{49} \times \sqrt{49} = \sqrt{49 \times 49} = \sqrt{2401}$. - Since $49 = 7^2$, $\sqrt{49} = 7$, so $7 \times 7 = 49$. 2. **Problem 1b:** Solve $(\sqrt{16})^2$. - The rule is $(\sqrt{a})^2 = a$. - So, $(\sqrt{16})^2 = 16$. 3. **Problem 2a:** Solve $\sqrt{2} \times 8$. - Multiply directly: $8 \times \sqrt{2}$. - This is simplified as $8\sqrt{2}$. 4. **Problem 2b:** Solve $\sqrt{36} - \sqrt{81}$. - Calculate each square root: $\sqrt{36} = 6$, $\sqrt{81} = 9$. - Subtract: $6 - 9 = -3$. 5. **Problem 3a:** Solve $\sqrt{91} - 27$. - $\sqrt{91}$ is approximately $9.54$ (since $9^2=81$ and $10^2=100$). - Subtract: $9.54 - 27 = -17.46$ approximately. 6. **Problem 3b:** Solve $\sqrt{\frac{490}{10}}$. - Simplify inside the root: $\frac{490}{10} = 49$. - So, $\sqrt{49} = 7$. 7. **Problem 4a:** Solve $\sqrt{24^2}$. - $\sqrt{a^2} = |a|$, so $\sqrt{24^2} = 24$. 8. **Problem 4b:** Solve $\sqrt{49} + \sqrt{100}$. - Calculate each root: $7 + 10 = 17$. 9. **Problem 5a:** Solve $\sqrt{49} + 0$. - $\sqrt{49} = 7$, so $7 + 0 = 7$. 10. **Problem 5b:** Solve $\sqrt{9} \times \sqrt{49}$. - Use property: $\sqrt{9} \times \sqrt{49} = \sqrt{9 \times 49} = \sqrt{441} = 21$. 11. **Problem 6a:** Solve $\frac{\sqrt{100}}{\sqrt{4}}$. - Calculate roots: $\frac{10}{2} = 5$. 12. **Problem 6b:** Solve $(\sqrt{100})^2$. - $(\sqrt{100})^2 = 100$. **Final answers:** 1a. 49 1b. 16 2a. $8\sqrt{2}$ 2b. -3 3a. Approximately -17.46 3b. 7 4a. 24 4b. 17 5a. 7 5b. 21 6a. 5 6b. 100