1. \( 2 \sqrt{8 x^{3}}-\sqrt{50 x}+3 \sqrt{2 x^{5}} \) 2. \( \sqrt{48}-\sqrt{12}+\sqrt{27} \) 3. \( 5 \sqrt{3}-2 \sqrt{12}-\sqrt{27} \)

To simplify the first expression, break down each term: 1. \( 2 \sqrt{8 x^{3}} = 2 \cdot 2\sqrt{2} \cdot x^{1.5} = 4\sqrt{2}x\sqrt{x} \) 2. \( \sqrt{50 x} = \sqrt{25 \cdot 2 \cdot x} = 5\sqrt{2x} \) 3. \( 3 \sqrt{2 x^{5}} = 3 \cdot \sqrt{2} \cdot x^{2.5} = 3\sqrt{2}x^2\sqrt{x} \) Putting it all together results in a combination of \(\sqrt{2}\) terms that makes the expression easier to interpret. In the second expression, we simplify step by step: 1. \( \sqrt{48} = 4\sqrt{3} \) 2. \( \sqrt{12} = 2\sqrt{3} \) 3. \( \sqrt{27} = 3\sqrt{3} \) Adding and subtracting yields \(4\sqrt{3} - 2\sqrt{3} + 3\sqrt{3} = (4 - 2 + 3)\sqrt{3} = 5\sqrt{3}\). Let's tackle the third expression! We have: \( 5\sqrt{3} - 2\sqrt{12} - \sqrt{27} \). Breaking it down: 1. \( \sqrt{12} = 2\sqrt{3} \), so \( -2\sqrt{12} = -4\sqrt{3} \). 2. \( \sqrt{27} = 3\sqrt{3} \). Combining all terms gives \( 5\sqrt{3} - 4\sqrt{3} - 3\sqrt{3} = (5 - 4 - 3)\sqrt{3} = -2\sqrt{3} \).