Kopertina e librit Matematika 10 - 11: Pjesa II

Zgjidhja e ushtrimit 9

Zgjidhja e ushtrimit 9 të mësimit 1.3A në librin Matematika 10 - 11: Pjesa II nga shtëpia botuese Botime Pegi me autorë Steve Fearnley, June Haighton, Steve Lomax, Peter Mullarkey, James Nicholson dhe Matt Nixon.

Pyetja

Paraqitni më thjesht shprehjet e mëposhtme.

  1. 18×2754\dfrac{\sqrt{18} \times \sqrt{27}}{\sqrt{54}}
  2. 98×1248×128\dfrac{\sqrt{98} \times \sqrt{12}}{\sqrt{48} \times \sqrt{128}}
  3. 810:24518\dfrac{\sqrt{8}}{\sqrt{10}} : \dfrac{2\sqrt{45}}{\sqrt{18}}
  4. 3210+850\dfrac{3\sqrt{2}}{10} + \dfrac{\sqrt{8}}{\sqrt{50}}
  5. 46315−3421024\dfrac{4\sqrt{63}}{15} - \dfrac{3\sqrt{42}}{10\sqrt{24}}
  6. 6528:39235\dfrac{65}{28} : \dfrac{39}{2\sqrt{35}}

Dëshiron të blesh libra manga?

Kliko këtu për të parë ofertat e Kleptobuk

Zgjidhja

  1. 18×27:54=9=3\sqrt{18 \times 27 : 54} = \sqrt{9} = 3
  2. 98×1248×128\dfrac{\sqrt{98 \times 12}}{\sqrt{48 \times 128}} == 49×2×1224×2×128\dfrac{\sqrt{49 \times 2 \times 12}}{\sqrt{24 \times 2 \times 128}} == 49×24256×24\dfrac{\sqrt{49} \times \sqrt{24}}{\sqrt{256} \times \sqrt{24}} == 7×2416×24\dfrac{7 \times \cancel{\sqrt{24}}}{16 \times \cancel{\sqrt{24}}} == 716\dfrac{7}{16}
  3. 810×18245=4×210×9×229×5=2210×3265=6×(2)2610×5=12625×2=225×2=252⇒252×5252=10250=25\dfrac{\sqrt{8}}{\sqrt{10}} \times \dfrac{\sqrt{18}}{2\sqrt{45}} = \dfrac{\sqrt{4 \times 2}}{\sqrt{10}} \times \dfrac{\sqrt{9\times 2}}{2\sqrt{9\times5}} = \dfrac{2\sqrt{2}}{\sqrt{10}} \times \dfrac{3\sqrt{2}}{6\sqrt{5}}= \dfrac{6\times(\sqrt{2})^2}{6\sqrt{10\times5}} = \dfrac{12}{6\sqrt{25\times 2}} = \dfrac{2}{\sqrt{25} \times \sqrt{2}} = \dfrac{2}{5\sqrt{2}} \rArr \dfrac{2}{5\sqrt{2}} \times \dfrac{5\sqrt{2}}{5\sqrt{2}} = \dfrac{10\sqrt{2}}{50} = \dfrac{\sqrt{2}}{5}
  4. 3210+4×225×2=3210+2252=3210+2252=32+410\dfrac{3\sqrt{2}}{10} + \dfrac{\sqrt{4 \times 2}}{\sqrt{25 \times 2}} = \dfrac{3\sqrt{2}}{10} + \dfrac{2\sqrt{2}}{5\sqrt{2}} = \dfrac{3\sqrt{2}}{10} + \dfrac{2\cancel{\sqrt{2}}}{5\cancel{\sqrt{2}}} = \dfrac{3\sqrt{2}+4}{10}
  5. 49×715−37×6106×4=12715−3×7×6206=12715−3720=13720\dfrac{4\sqrt{9 \times 7}}{15} - \dfrac{3\sqrt{7 \times 6}}{10\sqrt{6\times 4}} = \dfrac{12\sqrt{7}}{15} - \dfrac{3\times \sqrt{7} \times \cancel{\sqrt{6}}}{20\cancel{\sqrt{6}}} = \dfrac{12\sqrt{7}}{15} - \dfrac{3\sqrt{7}}{20} = \dfrac{13\sqrt{7}}{20}
  6. 13×57×4×27×513×3=13×527×2×7×513×3=53⇒53×33=533\dfrac{\sqrt{13 \times 5}}{\sqrt{7 \times 4}} \times \dfrac{2\sqrt{7 \times 5}}{\sqrt{13 \times 3}} = \dfrac{\cancel{\sqrt{13}} \times \sqrt{5}}{\cancel{2\sqrt{7}}} \times \dfrac{\cancel{2\times \sqrt{7}} \times \sqrt{5}}{\cancel{\sqrt{13}} \times \sqrt{3}} = \dfrac{5}{\sqrt{3}} \rArr \dfrac{5}{\sqrt{3}} \times \dfrac{\sqrt{3}}{\sqrt{3}} = \dfrac{5\sqrt{3}}{3}