Решение задач 7-11

Ниже представлено решение заданий с 7 по 11 из вашего учебника. Решения оформлены так, чтобы их было удобно переписать в тетрадь. Задание 8. Hisoblang (Вычислите): 1) \(\sqrt{2^8} = 2^{8/2} = 2^4 = 16\) 2) \(\sqrt{3^6} = 3^{6/2} = 3^3 = 27\) 3) \(\sqrt{5^4} = 5^{4/2} = 5^2 = 25\) 4) \(\sqrt{6^6} = 6^{6/2} = 6^3 = 216\) 5) \(\sqrt{(-3)^6} = \sqrt{3^6} = 3^3 = 27\) 6) \(\sqrt{(-7)^4} = \sqrt{7^4} = 7^2 = 49\) Задание 9. Ko'paytuvchini ildiz belgisi ostiga kiriting (Внесите множитель под знак корня): 1) \(2\sqrt{2} = \sqrt{2^2 \cdot 2} = \sqrt{4 \cdot 2} = \sqrt{8}\) 2) \(3\sqrt{3} = \sqrt{3^2 \cdot 3} = \sqrt{9 \cdot 3} = \sqrt{27}\) 3) \(2\sqrt{\frac{7}{2}} = \sqrt{2^2 \cdot \frac{7}{2}} = \sqrt{4 \cdot \frac{7}{2}} = \sqrt{2 \cdot 7} = \sqrt{14}\) Задание 10. Hisoblang (Вычислите): 1) \(\frac{4\sqrt{72}}{3\sqrt{8}} = \frac{4}{3} \sqrt{\frac{72}{8}} = \frac{4}{3} \sqrt{9} = \frac{4}{3} \cdot 3 = 4\) 2) \(\frac{2\sqrt{63}}{\sqrt{28}} = 2 \sqrt{\frac{63}{28}} = 2 \sqrt{\frac{9 \cdot 7}{4 \cdot 7}} = 2 \sqrt{\frac{9}{4}} = 2 \cdot \frac{3}{2} = 3\) 3) \(\frac{2\sqrt{45}}{\sqrt{80}} = 2 \sqrt{\frac{45}{80}} = 2 \sqrt{\frac{9 \cdot 5}{16 \cdot 5}} = 2 \sqrt{\frac{9}{16}} = 2 \cdot \frac{3}{4} = \frac{3}{2} = 1,5\) 4) \(\frac{4\sqrt{99}}{9\sqrt{44}} = \frac{4}{9} \sqrt{\frac{99}{44}} = \frac{4}{9} \sqrt{\frac{9 \cdot 11}{4 \cdot 11}} = \frac{4}{9} \sqrt{\frac{9}{4}} = \frac{4}{9} \cdot \frac{3}{2} = \frac{2}{3}\) Задание 11. Hisoblang (Вычислите): 1) \(2\sqrt{3} \cdot 27 - 6\sqrt{2 \cdot 18} = 54\sqrt{3} - 6\sqrt{36} = 54\sqrt{3} - 6 \cdot 6 = 54\sqrt{3} - 36\) 2) \(\sqrt{2^2 + 3 \cdot 7} = \sqrt{4 + 21} = \sqrt{25} = 5\) 3) \(\sqrt{17^2 - 15^2} = \sqrt{(17-15)(17+15)} = \sqrt{2 \cdot 32} = \sqrt{64} = 8\) 4) \(3\sqrt{121} - 2\sqrt{144} = 3 \cdot 11 - 2 \cdot 12 = 33 - 24 = 9\) 5) \(\sqrt{3^6} = 3^3 = 27\) 6) \(\sqrt{5^4} = 5^2 = 25\) 7) \(\sqrt{(-5)^6} = 5^3 = 125\) 8) \(\sqrt{(-3)^4} = 3^2 = 9\) 9) \(\sqrt{(-25)^2} = 25\) 10) \(\sqrt{49 \cdot 25} = \sqrt{49} \cdot \sqrt{25} = 7 \cdot 5 = 35\) 11) \(\sqrt{0,01 \cdot 169} = \sqrt{0,01} \cdot \sqrt{169} = 0,1 \cdot 13 = 1,3\) 12) \(\sqrt{625 \cdot 9 \cdot 36} = \sqrt{625} \cdot \sqrt{9} \cdot \sqrt{36} = 25 \cdot 3 \cdot 6 = 450\) 13) \(\sqrt{108 \cdot 27} = \sqrt{36 \cdot 3 \cdot 27} = \sqrt{36 \cdot 81} = 6 \cdot 9 = 54\) 14) \(\sqrt{27 \cdot 12} = \sqrt{9 \cdot 3 \cdot 3 \cdot 4} = \sqrt{9 \cdot 9 \cdot 4} = 3 \cdot 3 \cdot 2 = 18\) 15) \(\sqrt{2} \cdot \sqrt{32} = \sqrt{64} = 8\) 16) \(\sqrt{3} \cdot \sqrt{7} \cdot \sqrt{21} = \sqrt{21} \cdot \sqrt{21} = 21\) 17) \(\sqrt{2} \cdot \sqrt{22} \cdot \sqrt{11} = \sqrt{2 \cdot 22 \cdot 11} = \sqrt{484} = 22\) 18) \(\sqrt{\frac{1}{2}} \cdot \sqrt{\frac{2}{3}} \cdot \sqrt{3} = \sqrt{\frac{1 \cdot 2 \cdot 3}{2 \cdot 3}} = \sqrt{1} = 1\)