1. Calculate the following expressions involving square roots. 2. Use the property \(\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}\) to simplify each fraction. 3. Simplify each square root by factoring out perfect squares. 4. a. \(\frac{\sqrt{27}}{\sqrt{3}} = \sqrt{\frac{27}{3}} = \sqrt{9} = 3\) 5. b. \(\frac{\sqrt{12}}{\sqrt{3}} = \sqrt{\frac{12}{3}} = \sqrt{4} = 2\) 6. c. \(\frac{\sqrt{14}}{\sqrt{7}} = \sqrt{\frac{14}{7}} = \sqrt{2}\) 7. d. \(\frac{-\sqrt{15}}{\sqrt{3}} = -\sqrt{\frac{15}{3}} = -\sqrt{5}\) 8. Convert each expression to a single square root form using \(a\sqrt{b} = \sqrt{a^2 b}\). 9. a. \(4\sqrt{2} = \sqrt{4^2 \times 2} = \sqrt{16 \times 2} = \sqrt{32}\) 10. b. \(5\sqrt{3} = \sqrt{5^2 \times 3} = \sqrt{25 \times 3} = \sqrt{75}\) 11. c. \(-3\sqrt{7} = -\sqrt{3^2 \times 7} = -\sqrt{9 \times 7} = -\sqrt{63}\) 12. d. \(7\sqrt{6} = \sqrt{7^2 \times 6} = \sqrt{49 \times 6} = \sqrt{294}\) Final answers: - 1a: 3 - 1b: 2 - 1c: \(\sqrt{2}\) - 1d: \(-\sqrt{5}\) - 2a: \(\sqrt{32}\) - 2b: \(\sqrt{75}\) - 2c: \(-\sqrt{63}\) - 2d: \(\sqrt{294}\)