Đáp án:

Giải thích các bước giải:

 `a) -\sqrt{242} + \sqrt{288} - 5\sqrt{2} + 3\sqrt{338} = -\sqrt{121 \cdot 2} + \sqrt{144 \cdot 2} - 5\sqrt{2} + 3\sqrt{169 \cdot 2}` 

`= -11\sqrt{2} + 12\sqrt{2} - 5\sqrt{2} + 3 \cdot 13\sqrt{2} = -11\sqrt{2} + 12\sqrt{2} - 5\sqrt{2} + 39\sqrt{2}`

`= (-11 + 12 - 5 + 39)\sqrt{2} = 35\sqrt{2}`

`b) 10\sqrt{72} - \frac{5}{3}\sqrt{162} + \sqrt{128} - 2\sqrt{50} + \sqrt{98} = 10\sqrt{36 \cdot 2} - \frac{5}{3}\sqrt{81 \cdot 2} + \sqrt{64 \cdot 2} - 2\sqrt{25 \cdot 2} + \sqrt{49 \cdot 2}`

`= 10 \cdot 6\sqrt{2} - \frac{5}{3} \cdot 9\sqrt{2} + 8\sqrt{2} - 2 \cdot 5\sqrt{2} + 7\sqrt{2} = 60\sqrt{2} - 15\sqrt{2} + 8\sqrt{2} - 10\sqrt{2} + 7\sqrt{2}`

`= (60 - 15 + 8 - 10 + 7)\sqrt{2} = 50\sqrt{2}`

`c) \frac{1}{9}\sqrt{162} - \frac{3}{4}\sqrt{128} + \frac{12}{13}\sqrt{338} - \frac{7}{24}\sqrt{288} = \frac{1}{9}\sqrt{81 \cdot 2} - \frac{3}{4}\sqrt{64 \cdot 2} + \frac{12}{13}\sqrt{169 \cdot 2} - \frac{7}{24}\sqrt{144 \cdot 2}`

`= \frac{1}{9} \cdot 9\sqrt{2} - \frac{3}{4} \cdot 8\sqrt{2} + \frac{12}{13} \cdot 13\sqrt{2} - \frac{7}{24} \cdot 12\sqrt{2} = \sqrt{2} - 6\sqrt{2} + 12\sqrt{2} - \frac{7}{2}\sqrt{2}`

`= (1 - 6 + 12 - \frac{7}{2})\sqrt{2} = (7 - \frac{7}{2})\sqrt{2} = \frac{7}{2}\sqrt{2}`

`d) 2\sqrt{147} - \frac{3}{32}\sqrt{192} + \frac{4}{18}\sqrt{243} - \frac{1}{10}\sqrt{300} = 2\sqrt{49 \cdot 3} - \frac{3}{32}\sqrt{64 \cdot 3} + \frac{2}{9}\sqrt{81 \cdot 3} - \frac{1}{10}\sqrt{100 \cdot 3}`

`= 14\sqrt{3} - \frac{3}{4}\sqrt{3} + 2\sqrt{3} - \sqrt{3} = (14 - \frac{3}{4} + 2 - 1)\sqrt{3} = (15 - \frac{3}{4})\sqrt{3} = \frac{57}{4}\sqrt{3}`

`e) \frac{5}{8}\sqrt{48} - \frac{1}{33}\sqrt{363} + \frac{3}{14}\sqrt{147} - \frac{1}{4}\sqrt{192} = \frac{5}{8}\sqrt{16 \cdot 3} - \frac{1}{33}\sqrt{121 \cdot 3} + \frac{3}{14}\sqrt{49 \cdot 3} - \frac{1}{4}\sqrt{64 \cdot 3}`

`= \frac{5}{8} \cdot 4\sqrt{3} - \frac{1}{33} \cdot 11\sqrt{3} + \frac{3}{14} \cdot 7\sqrt{3} - \frac{1}{4} \cdot 8\sqrt{3} = \frac{5}{2}\sqrt{3} - \frac{1}{3}\sqrt{3} + \frac{3}{2}\sqrt{3} - 2\sqrt{3}`

`= (4 - \frac{1}{3} - 2)\sqrt{3} = (2 - \frac{1}{3})\sqrt{3} = \frac{5}{3}\sqrt{3}`