ចំនួនអសនិទាន - Hw-03

ប្រមាណវិធីលើរ៉ាឌីកាល់- កម្រិតមធ្យម

ប្រធានលំហាត់

ចូរគណនា និងសម្រួលកន្សោមរ៉ាឌីកាល់ខាងក្រោម៖

• 1. $A = 2\sqrt{48} - 3\sqrt{27} + \sqrt{75}$
• 2. $B = 5\sqrt{72} - 4\sqrt{98} + 2\sqrt{50}$
• 3. $C = \frac{1}{2}\sqrt{128} + \frac{2}{3}\sqrt{162} - \sqrt{200}$
• 4. $D = \sqrt{125} - 2\sqrt{20} + 3\sqrt{45} - \sqrt{80}$
• 5. $E = 3\sqrt{14} \times 2\sqrt{21}$
• 6. $F = (3\sqrt{2} - 2\sqrt{3})(2\sqrt{2} + \sqrt{3})$
• 7. $G = 2\sqrt{3}(\sqrt{27} - 2\sqrt{12} + \sqrt{6})$
• 8. $H = (3\sqrt{5} - 2\sqrt{2})(3\sqrt{5} + 2\sqrt{2})$
• 9. $I = \frac{4\sqrt{150}}{3\sqrt{6}}$
• 10. $J = \frac{12\sqrt{15}}{4\sqrt{5}} \times \sqrt{27}$
• 11. $K = \frac{2\sqrt{18} \times 3\sqrt{10}}{4\sqrt{5}}$
• 12. $L = (2\sqrt{6} - \sqrt{3})^{2}$
• 13. $M = \sqrt{243} - \frac{6}{\sqrt{3}} + \sqrt{12}$

---

ចម្លើយ និងដំណោះស្រាយសង្ខេប

• 1. $A = 2(4\sqrt{3}) - 3(3\sqrt{3}) + 5\sqrt{3} = 8\sqrt{3} - 9\sqrt{3} + 5\sqrt{3} = 4\sqrt{3}$
• 2. $B = 5(6\sqrt{2}) - 4(7\sqrt{2}) + 2(5\sqrt{2}) = 30\sqrt{2} - 28\sqrt{2} + 10\sqrt{2} = 12\sqrt{2}$
• 3. $C = \frac{1}{2}(8\sqrt{2}) + \frac{2}{3}(9\sqrt{2}) - 10\sqrt{2} = 4\sqrt{2} + 6\sqrt{2} - 10\sqrt{2} = 0$
• 4. $D = 5\sqrt{5} - 2(2\sqrt{5}) + 3(3\sqrt{5}) - 4\sqrt{5} = 5\sqrt{5} - 4\sqrt{5} + 9\sqrt{5} - 4\sqrt{5} = 6\sqrt{5}$
• 5. $E = (3 \times 2)\sqrt{14 \times 21} = 6\sqrt{294} = 6\sqrt{49 \times 6} = 6(7\sqrt{6}) = 42\sqrt{6}$
• 6. $F = 6(\sqrt{4}) + 3\sqrt{6} - 4\sqrt{6} - 2(\sqrt{9}) = 12 - \sqrt{6} - 6 = 6 - \sqrt{6}$
• 7. $G = 2\sqrt{3}(3\sqrt{3} - 4\sqrt{3} + \sqrt{6}) = 2\sqrt{3}(-\sqrt{3} + \sqrt{6}) = -2(\sqrt{9}) + 2\sqrt{18} = -6 + 2(3\sqrt{2}) = -6 + 6\sqrt{2}$
• 8. $H = (3\sqrt{5})^{2} - (2\sqrt{2})^{2} = 9(5) - 4(2) = 45 - 8 = 37$
• 9. $I = (\frac{4}{3})\sqrt{\frac{150}{6}} = \frac{4}{3}\sqrt{25} = \frac{4}{3}(5) = \frac{20}{3}$
• 10. $J = (\frac{12}{4})\sqrt{\frac{15}{5}} \times \sqrt{27} = 3\sqrt{3} \times 3\sqrt{3} = 9(\sqrt{9}) = 9 \times 3 = 27$
• 11. $K = \frac{6\sqrt{180}}{4\sqrt{5}} = (\frac{6}{4})\sqrt{\frac{180}{5}} = \frac{3}{2}\sqrt{36} = \frac{3}{2}(6) = 9$
• 12. $L = (2\sqrt{6})^{2} - 2(2\sqrt{6})(\sqrt{3}) + (\sqrt{3})^{2} = 4(6) - 4\sqrt{18} + 3 = 24 - 4(3\sqrt{2}) + 3 = 27 - 12\sqrt{2}$
• 13. $M = \sqrt{81 \times 3} - \frac{6\sqrt{3}}{(\sqrt{3})^{2}} + \sqrt{4 \times 3}$
  $\phantom{M} = 9\sqrt{3} - \frac{6\sqrt{3}}{3} + 2\sqrt{3}$
  $\phantom{M} = 9\sqrt{3} - 2\sqrt{3} + 2\sqrt{3} = 9\sqrt{3}$