EXERCISE 5 (a) Simplify the following expressions, without the use of a calculator: (1) \( \sqrt{12}+\sqrt{27}-\sqrt{3} \) (2) \( \sqrt{18}-\sqrt{50}-\sqrt{32} \) (3) \( \sqrt{6} \times \sqrt{3} \) (4) \( \frac{\sqrt{75}}{\sqrt{3}} \) (5) \( (\sqrt{3}+\sqrt{12})^{2} \) (6) \( (\sqrt{3}+\sqrt{5})(\sqrt{3}-\sqrt{5}) \) (7) \( \sqrt{3}\left(\sqrt{12}-\sqrt{1 \frac{1}{3}}\right) \) (8) \( \frac{\sqrt{50}+\sqrt{2}}{\sqrt{18}} \) (9) \( \frac{6 \sqrt{8}+4 \sqrt{18}}{3 \sqrt{32}-\sqrt{72}} \) (10) \( \frac{2 \sqrt{12}+4 \sqrt{20}}{\sqrt{12}+\sqrt{80}} \) 38

Sure, let’s make those expressions a bit easier to digest! (1) \( \sqrt{12}+\sqrt{27}-\sqrt{3} = 2\sqrt{3} + 3\sqrt{3} - \sqrt{3} = 4\sqrt{3} \) (2) \( \sqrt{18}-\sqrt{50}-\sqrt{32} = 3\sqrt{2} - 5\sqrt{2} - 4\sqrt{2} = -6\sqrt{2} \) (3) \( \sqrt{6} \times \sqrt{3} = \sqrt{18} = 3\sqrt{2} \) (4) \( \frac{\sqrt{75}}{\sqrt{3}} = \sqrt{25} = 5 \) (5) \( (\sqrt{3}+\sqrt{12})^{2} = (\sqrt{3}+2\sqrt{3})^{2} = (3\sqrt{3})^{2} = 27 \) (6) \( (\sqrt{3}+\sqrt{5})(\sqrt{3}-\sqrt{5}) = 3 - 5 = -2 \) (7) \( \sqrt{3}(\sqrt{12}-\sqrt{1 \frac{1}{3}}) = \sqrt{3}(2\sqrt{3} - \frac{2}{3}) = \frac{10\sqrt{3}}{3} \) (8) \( \frac{\sqrt{50}+\sqrt{2}}{\sqrt{18}} = \frac{5\sqrt{2}+\sqrt{2}}{3\sqrt{2}} = \frac{6\sqrt{2}}{3\sqrt{2}} = 2 \) (9) \( \frac{6 \sqrt{8}+4 \sqrt{18}}{3 \sqrt{32}-\sqrt{72}} = \frac{12\sqrt{2}+12\sqrt{2}}{12-6} = \frac{24\sqrt{2}}{6} = 4\sqrt{2} \) (10) \( \frac{2 \sqrt{12}+4 \sqrt{20}}{\sqrt{12}+\sqrt{80}} = \frac{4\sqrt{3}+8\sqrt{5}}{4\sqrt{5}} = 1 + 2\frac{\sqrt{3}}{\sqrt{5}} \) Let me know if you want to explore more of these!