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8.6E: Mazoezi

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    176317

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    Mazoezi hufanya kamili

    Zoezi SET A: kugawanya mizizi ya mraba

    Katika mazoezi yafuatayo, kurahisisha.

    1. a.\(\dfrac{\sqrt{128}}{\sqrt{72}}\quad\) b.\(\dfrac{\sqrt[3]{128}}{\sqrt[3]{54}}\)

    2. a.\(\dfrac{\sqrt{48}}{\sqrt{75}}\quad\) b.\(\dfrac{\sqrt[3]{81}}{\sqrt[3]{24}}\)

    3. a.\(\dfrac{\sqrt{200 m^{5}}}{\sqrt{98 m}}\quad\) b.\(\dfrac{\sqrt[3]{54 y^{2}}}{\sqrt[3]{2 y^{5}}}\)

    4. a.\(\dfrac{\sqrt{108 n^{7}}}{\sqrt{243 n^{3}}}\quad\) b.\(\dfrac{\sqrt[3]{54 y}}{\sqrt[3]{16 y^{4}}}\)

    5. a.\(\dfrac{\sqrt{75 r^{3}}}{\sqrt{108 r^{7}}}\quad\) b.\(\dfrac{\sqrt[3]{24 x^{7}}}{\sqrt[3]{81 x^{4}}}\)

    6. a.\(\dfrac{\sqrt{196 q}}{\sqrt{484 q^{5}}}\quad\) b.\(\dfrac{\sqrt[3]{16 m^{4}}}{\sqrt[3]{54 m}}\)

    7. a.\(\dfrac{\sqrt{108 p^{5} q^{2}}}{\sqrt{3 p^{3} q^{6}}}\quad\) b.\(\dfrac{\sqrt[3]{-16 a^{4} b^{-2}}}{\sqrt[3]{2 a^{-2} b}}\)

    8. a.\(\dfrac{\sqrt{98 r s^{10}}}{\sqrt{2 r^{3} s^{4}}}\quad\) b.\(\dfrac{\sqrt[3]{-375 y^{4} z^{2}}}{\sqrt[3]{3 y^{-2} z^{4}}}\)

    9. a.\(\dfrac{\sqrt{320 m n^{-5}}}{\sqrt{45 m^{-7} n^{3}}}\quad\) b.\(\dfrac{\sqrt[3]{16 x^{4} y^{-2}}}{\sqrt[3]{-54 x^{-2} y^{4}}}\)

    10. a.\(\dfrac{\sqrt{810 c^{-3} d^{7}}}{\sqrt{1000 c d}}\quad\) b.\(\dfrac{\sqrt[3]{24 a^{7} b^{-1}}}{\sqrt[3]{-81 a^{-2} b^{2}}}\)

    11. \(\dfrac{\sqrt{56 x^{5} y^{4}}}{\sqrt{2 x y^{3}}}\)

    12. \(\dfrac{\sqrt{72 a^{3} b^{6}}}{\sqrt{3 a b^{3}}}\)

    13. \(\dfrac{\sqrt[3]{48 a^{3} b^{6}}}{\sqrt[3]{3 a^{-1} b^{3}}}\)

    14. \(\dfrac{\sqrt[3]{162 x^{-3} y^{6}}}{\sqrt[3]{2 x^{3} y^{-2}}}\)

    Jibu

    1. a.\(\dfrac{4}{3}\) b.\(\dfrac{4}{3}\)

    3. a.\(\dfrac{10 m^{2}}{7}\) b.\(\dfrac{3}{y}\)

    5. a.\(\dfrac{5}{6 r^{2}}\) b.\(\dfrac{2x}{3}\)

    7. a.\(\dfrac{6 p}{q^{2}}\) b.\(-\dfrac{2 a^{2}}{b}\)

    9. a.\(\dfrac{8 m^{4}}{3 n^{4}}\) b.\(-\dfrac{2 x^{2}}{3 y^{2}}\)

    11. \(4 x^{4} \sqrt{7 y}\)

    13. \(2 a b \sqrt[3]{2 a}\)

    Zoezi SET B: Rationalize Denominator Moja ya Muda

    Katika mazoezi yafuatayo, rationalize denominator.

    15. a.\(\dfrac{10}{\sqrt{6}}\quad\) b.\(\sqrt{\dfrac{4}{27}}\quad\) c.\(\dfrac{10}{\sqrt{5 x}}\)

    16. a.\(\dfrac{8}{\sqrt{3}}\quad\) b.\(\sqrt{\dfrac{7}{40}}\quad\) c.\(\dfrac{8}{\sqrt{2 y}}\)

    17. a.\(\dfrac{6}{\sqrt{7}}\quad\) b.\(\sqrt{\dfrac{8}{45}}\quad\) c.\(\dfrac{12}{\sqrt{3 p}}\)

    18. a.\(\dfrac{4}{\sqrt{5}}\quad\) b.\(\sqrt{\dfrac{27}{80}}\quad\) c.\(\dfrac{18}{\sqrt{6 q}}\)

    19. a.\(\dfrac{1}{\sqrt[3]{5}}\quad\) b.\(\sqrt[3]{\dfrac{5}{24}}\quad\) c.\(\dfrac{4}{\sqrt[3]{36 a}}\)

    20. a.\(\dfrac{1}{\sqrt[3]{3}}\quad\) b.\(\sqrt[3]{\dfrac{5}{32}}\quad\) c.\(\dfrac{7}{\sqrt[3]{49 b}}\)

    21. a.\(\dfrac{1}{\sqrt[3]{11}}\quad\) b.\(\sqrt[3]{\dfrac{7}{54}}\quad\) c.\(\dfrac{3}{\sqrt[3]{3 x^{2}}}\)

    22. a.\(\dfrac{1}{\sqrt[3]{13}}\quad\) b.\(\sqrt[3]{\dfrac{3}{128}}\quad\) c.\(\dfrac{3}{\sqrt[3]{6 y^{2}}}\)

    23. a.\(\dfrac{1}{\sqrt[4]{7}}\quad\) b.\(\sqrt[4]{\dfrac{5}{32}}\quad\) c.\(\dfrac{4}{\sqrt[4]{4 x^{2}}}\)

    24. a.\(\dfrac{1}{\sqrt[4]{4}}\quad\) b.\(\sqrt[4]{\dfrac{9}{32}}\quad\) c.\(\dfrac{6}{\sqrt[4]{9 x^{3}}}\)

    25. a.\(\dfrac{1}{\sqrt[4]{9}}\quad\) b.\(\sqrt[4]{\dfrac{25}{128}}\quad\) c.\(\dfrac{6}{\sqrt[4]{27 a}}\)

    26. a.\(\dfrac{1}{\sqrt[4]{8}}\quad\) b.\(\sqrt[4]{\dfrac{27}{128}}\quad\) c.\(\dfrac{16}{\sqrt[4]{64 b^{2}}}\)

    Jibu

    15. a.\(\dfrac{5 \sqrt{6}}{3}\) b.\(\dfrac{2 \sqrt{3}}{9}\) c.\(\dfrac{2 \sqrt{5 x}}{x}\)

    17. a.\(\dfrac{6 \sqrt{7}}{7}\) b.\(\dfrac{2 \sqrt{10}}{15}\) c.\(\dfrac{4 \sqrt{3 p}}{p}\)

    19. a.\(\dfrac{\sqrt[3]{25}}{5}\) b.\(\dfrac{\sqrt[3]{45}}{6}\) c.\(\dfrac{2 \sqrt[3]{6 a^{2}}}{3 a}\)

    21. a.\(\dfrac{\sqrt[3]{121}}{11}\) b.\(\dfrac{\sqrt[3]{28}}{6}\) c.\(\dfrac{\sqrt[3]{9 x}}{x}\)

    23. a.\(\dfrac{\sqrt[4]{343}}{7}\) b.\(\dfrac{\sqrt[4]{40}}{4}\) c.\(\dfrac{2 \sqrt[4]{4 x^{2}}}{x}\)

    25. a.\(\dfrac{\sqrt[4]{9}}{3}\) b.\(\dfrac{\sqrt[4]{50}}{4}\) c.\(\dfrac{2 \sqrt[4]{3 a^{2}}}{a}\)

    Zoezi SET C: Rationalize Denominator ya Muda Mbili

    Katika mazoezi yafuatayo, kurahisisha.

    27. \(\dfrac{8}{1-\sqrt{5}}\)

    28. \(\dfrac{7}{2-\sqrt{6}}\)

    29. \(\dfrac{6}{3-\sqrt{7}}\)

    30. \(\dfrac{5}{4-\sqrt{11}}\)

    31. \(\dfrac{\sqrt{3}}{\sqrt{m}-\sqrt{5}}\)

    32. \(\dfrac{\sqrt{5}}{\sqrt{n}-\sqrt{7}}\)

    33. \(\dfrac{\sqrt{2}}{\sqrt{x}-\sqrt{6}}\)

    34. \(\dfrac{\sqrt{7}}{\sqrt{y}+\sqrt{3}}\)

    35. \(\dfrac{\sqrt{r}+\sqrt{5}}{\sqrt{r}-\sqrt{5}}\)

    36. \(\dfrac{\sqrt{s}-\sqrt{6}}{\sqrt{s}+\sqrt{6}}\)

    37. \(\dfrac{\sqrt{x}+\sqrt{8}}{\sqrt{x}-\sqrt{8}}\)

    38. \(\dfrac{\sqrt{m}-\sqrt{3}}{\sqrt{m}+\sqrt{3}}\)

    Jibu

    27. \(-2(1+\sqrt{5})\)

    29. \(3(3+\sqrt{7})\)

    31. \(\dfrac{\sqrt{3}(\sqrt{m}+\sqrt{5})}{m-5}\)

    33. \(\dfrac{\sqrt{2}(\sqrt{x}+\sqrt{6})}{x-6}\)

    35. \(\dfrac{(\sqrt{r}+\sqrt{5})^{2}}{r-5}\)

    37. \(\dfrac{(\sqrt{x}+2 \sqrt{2})^{2}}{x-8}\)

    Zoezi SET D: mazoezi ya kuandika
      1. Kurahisisha\(\sqrt{\dfrac{27}{3}}\) na kuelezea hatua zako zote.
      2. Kurahisisha\(\sqrt{\dfrac{27}{5}}\) na kuelezea hatua zako zote.
      3. Kwa nini njia mbili za kurahisisha mizizi ya mraba tofauti?
    2. Eleza nini maana ya neno rationalize katika maneno, “rationalize denominator.”
    3. Eleza kwa nini kuzidisha\(\sqrt{2x}-3\) kwa matokeo yake ya conjugate kwa kujieleza na hakuna radicals.
    4. Eleza kwa nini kuzidisha\(\dfrac{7}{\sqrt[3]{x}}\) kwa\(\dfrac{\sqrt[3]{x}}{\sqrt[3]{x}}\) haina rationalize denominator.
    Jibu

    1. Majibu yatatofautiana

    3. Majibu yatatofautiana

    Self Check

    Baada ya kukamilisha mazoezi, tumia orodha hii ili kutathmini ujuzi wako wa malengo ya sehemu hii.

    Jedwali hili lina safu 4 na nguzo 4. Mstari wa kwanza ni mstari wa kichwa na huandika kila safu. Kichwa cha kwanza cha safu ni â € naweza â € €, pili ni â € € confidentlyâ €, ya tatu ni â € € na baadhi ya msaada â € €, na ya nne ni â € no, mimi donâ €™ t kupata hiyo €. Chini ya safu ya kwanza ni maneno â € kugawanya maneno makubwa. â €, â € rationalize neno moja denominatorâ €, na â € rationalize denominatorâ neno mbili €. Nguzo nyingine zimeachwa tupu ili mwanafunzi aweze kuonyesha kiwango chao cha ustadi kwa kila mada.
    Kielelezo 8.5.63

    b Baada ya kuangalia orodha, unafikiri umeandaliwa vizuri kwa sehemu inayofuata? Kwa nini au kwa nini?