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8.2E: Mazoezi

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    176294

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    Kurahisisha Maneno na Mizizi

    Katika mazoezi yafuatayo, kurahisisha.

    1. a.\(\sqrt{64}\) b.\(-\sqrt{81}\)

    Jibu

    a.\(8\) b.\(-9\)

    2. a.\(\sqrt{169}\) b.\(-\sqrt{100}\)

    3. a.\(\sqrt{196}\) b.\(-\sqrt{1}\)

    Jibu

    a.\(14\) b.\(-1\)

    4. a.\(\sqrt{144}\) b.\(-\sqrt{121}\)

    5. a.\(\sqrt{\frac{4}{9}}\) b.\(-\sqrt{0.01}\)

    Jibu

    a.\(\frac{2}{3}\) b.\(-0.1\)

    6. a.\(\sqrt{\frac{64}{121}}\) b.\(-\sqrt{0.16}\)

    7. a.\(\sqrt{-121}\) b.\(-\sqrt{289}\)

    Jibu

    a. si idadi halisi b.\(-17\)

    8. a.\(-\sqrt{400}\) b.\(\sqrt{-36}\)

    9. a.\(-\sqrt{225}\) b.\(\sqrt{-9}\)

    Jibu

    a.\(-15\) b. si idadi halisi

    10. a.\(\sqrt{-49}\) b.\(-\sqrt{256}\)

    11. a.\(\sqrt[3]{216}\) b.\(\sqrt[4]{256}\)

    Jibu

    a.\(6\) b.\(4\)

    12. a.\(\sqrt[3]{27}\) b.\(\sqrt[4]{16}\) c.\(\sqrt[5]{243}\)

    13. a.\(\sqrt[3]{512}\) b.\(\sqrt[4]{81}\) c.\(\sqrt[5]{1}\)

    Jibu

    a.\(8\) b.\(3\) b.\(1\)

    14. a.\(\sqrt[3]{125}\) b.\(\sqrt[4]{1296}\) c.\(\sqrt[5]{1024}\)

    15. a.\(\sqrt[3]{-8}\) b.\(\sqrt[4]{-81}\) c.\(\sqrt[5]{-32}\)

    Jibu

    a.\(-2\) b. si idadi halisi c.\(-2\)

    16. a.\(\sqrt[3]{-64}\) b.\(\sqrt[4]{-16}\) c.\(\sqrt[5]{-243}\)

    17. a.\(\sqrt[3]{-125}\) b.\(\sqrt[4]{-1296}\) c.\(\sqrt[5]{-1024}\)

    Jibu

    a.\(-5\) b. si idadi halisi c.\(-4\)

    18. a.\(\sqrt[3]{-512}\) b.\(\sqrt[4]{-81}\) c.\(\sqrt[5]{-1}\)

    Katika mazoezi yafuatayo, tathmini kila mizizi kwa kutoa muda wa namba mbili za mfululizo ambazo mizizi iko.

    19. a.\(\sqrt{70}\) b.\(\sqrt[3]{71}\)

    Jibu

    a.\(8<\sqrt{70}<9\) b.\(4<\sqrt[3]{71}<5\)

    20. a.\(\sqrt{55}\) b.\(\sqrt[3]{119}\)

    21. a.\(\sqrt{200}\) b.\(\sqrt[3]{137}\)

    Jibu

    a.\(14<\sqrt{200}<15\) b.\(5<\sqrt[3]{137}<6\)

    22. a.\(\sqrt{172}\) b.\(\sqrt[3]{200}\)

    Katika mazoezi yafuatayo, takriban kila mizizi na pande zote kwa maeneo mawili ya decimal.

    23. a.\(\sqrt{19}\) b.\(\sqrt[3]{89}\) c.\(\sqrt[4]{97}\)

    Jibu

    a.\(\approx 4.36\) b.\(\approx 4.46\) c.\(\approx 3.14\)

    24. a.\(\sqrt{21}\) b.\(\sqrt[3]{93}\) c.\(\sqrt[4]{101}\)

    25. a.\(\sqrt{53}\) b.\(\sqrt[3]{147}\) c.\(\sqrt[4]{452}\)

    Jibu

    a.\(\approx 7.28\) b.\(\approx 5.28\) c.\(\approx 4.61\)

    26. a.\(\sqrt{47}\) b.\(\sqrt[3]{163}\) c.\(\sqrt[4]{527}\)

    Punguza Maneno ya kutofautiana na Mizizi

    Katika mazoezi yafuatayo, kurahisisha kutumia maadili kamili kama inavyohitajika.

    27. a.\(\sqrt[5]{u^{5}}\) b.\(\sqrt[8]{v^{8}}\)

    Jibu

    a.\(u\) b.\(|v|\)

    28. a.\(\sqrt[3]{a^{3}}\) b.\(\sqrt[9]{b^{9}}\)

    29. a.\(\sqrt[4]{y^{4}}\) b.\(\sqrt[7]{m^{7}}\)

    Jibu

    a.\(|y|\) b.\(m\)

    30. a.\(\sqrt[8]{k^{8}}\) b.\(\sqrt[6]{p^{6}}\)

    31. a.\(\sqrt{x^{6}}\) b.\(\sqrt{y^{16}}\)

    Jibu

    a.\(|x^{3}|\) b.\(y^{8}\)

    32. a.\(\sqrt{a^{14}}\) b.\(\sqrt{w^{24}}\)

    33. a.\(\sqrt{x^{24}}\) b.\(\sqrt{y^{22}}\)

    Jibu

    a.\(x^{12}\) b.\(|y^{11}|\)

    34. a.\(\sqrt{a^{12}}\) b.\(\sqrt{b^{26}}\)

    35. a.\(\sqrt[3]{x^{9}}\) b.\(\sqrt[4]{y^{12}}\)

    Jibu

    a.\(x^{3}\) b.\(|y^{3}|\)

    36. a.\(\sqrt[5]{a^{10}}\) b.\(\sqrt[3]{b^{27}}\)

    37. a.\(\sqrt[4]{m^{8}}\) b.\(\sqrt[5]{n^{20}}\)

    Jibu

    a.\(m^{2}\) b.\(n^{4}\)

    38. a.\(\sqrt[6]{r^{12}}\) b.\(\sqrt[3]{s^{30}}\)

    39. a.\(\sqrt{49 x^{2}}\) b.\(-\sqrt{81 x^{18}}\)

    Jibu

    a.\(7|x|\) b.\(-9|x^{9}|\)

    40. a.\(\sqrt{100 y^{2}}\) b.\(-\sqrt{100 m^{32}}\)

    41. a.\(\sqrt{121 m^{20}}\) b.\(-\sqrt{64 a^{2}}\)

    Jibu

    a.\(11m^{10}\) b.\(-8|a|\)

    42. a.\(\sqrt{81 x^{36}}\) b.\(-\sqrt{25 x^{2}}\)

    43. a.\(\sqrt[4]{16 x^{8}}\) b.\(\sqrt[6]{64 y^{12}}\)

    Jibu

    a.\(2x^{2}\) b.\(2y^{2}\)

    44. a.\(\sqrt[3]{-8 c^{9}}\) b.\(\sqrt[3]{125 d^{15}}\)

    45. a.\(\sqrt[3]{216 a^{6}}\) b.\(\sqrt[5]{32 b^{20}}\)

    Jibu

    a.\(6a^{2}\) b.\(2b^{4}\)

    46. a.\(\sqrt[7]{128 r^{14}}\) b.\(\sqrt[4]{81 s^{24}}\)

    47. a.\(\sqrt{144 x^{2} y^{2}}\) b.\(\sqrt{169 w^{8} y^{10}}\) c.\(\sqrt[3]{8 a^{51} b^{6}}\)

    Jibu

    a.\(12|x y|\) b.\(13 w^{4}\left|y^{5}\right|\) c.\(2 a^{17} b^{2}\)

    48. a.\(\sqrt{196 a^{2} b^{2}}\) b.\(\sqrt{81 p^{24} q^{6}}\) c.\(\sqrt[3]{27 p^{45} q^{9}}\)

    49. a.\(\sqrt{121 a^{2} b^{2}}\) b.\(\sqrt{9 c^{8} d^{12}}\) c.\(\sqrt[3]{64 x^{15} y^{66}}\)

    Jibu

    a.\(11|ab|\) b.\(3c^{4}d^{6}\) c.\(4x^{5}y^{22}\)

    50. a.\(\sqrt{225 x^{2} y^{2} z^{2}}\) b.\(\sqrt{36 r^{6} s^{20}}\) c.\(\sqrt[3]{125 y^{18} z^{27}}\)

    Mazoezi ya kuandika

    51. Kwa nini hakuna idadi halisi sawa na\(\sqrt{-64}\)?

    Jibu

    Kwa kuwa mraba wa idadi yoyote halisi ni chanya, haiwezekani kwa idadi halisi ya mraba kwa\(-64\).

    52. Ni tofauti gani kati ya\(9^{2}\) na\(\sqrt{9}\)?

    53. Eleza nini maana ya\(n^{th}\) mzizi wa idadi.

    Jibu

    Ikiwa utainua mizizi hii kwa\(n^{th}\) nguvu, itakupa nambari ya awali (chini ya radical).

    54. Eleza tofauti ya kutafuta\(n^{th}\) mizizi ya namba wakati index ni hata ikilinganishwa na wakati index ni isiyo ya kawaida.

    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 € kurahisisha maneno na mizizi.â €, â € makisio na takriban mizizi â €, na â € kurahisisha maneno variable na mizizi â €. Nguzo nyingine zimeachwa tupu ili mwanafunzi aweze kuonyesha kiwango chao cha ustadi kwa kila mada.

    b Kama wengi wa hundi yako walikuwa:

    ... kwa ujasiri. Hongera! Umefanikiwa malengo katika sehemu hii. Fikiria ujuzi wa kujifunza uliyotumia ili uweze kuendelea kuitumia. Ulifanya nini ili uwe na ujasiri wa uwezo wako wa kufanya mambo haya? Kuwa maalum.

    ... kwa msaada fulani. Hii lazima kushughulikiwa haraka kwa sababu mada huna bwana kuwa mashimo katika barabara yako ya mafanikio. Katika hesabu kila mada hujenga juu ya kazi ya awali. Ni muhimu kuhakikisha kuwa na msingi imara kabla ya kuendelea. Nani unaweza kuomba msaada? Washiriki wenzako na mwalimu ni rasilimali nzuri. Je, kuna mahali kwenye chuo ambapo waalimu hisabati zinapatikana? Je, ujuzi wako wa kujifunza unaweza kuboreshwa?

    ... hapana - Siipati! Hii ni ishara ya onyo na haipaswi kupuuza. Unapaswa kupata msaada mara moja au utazidiwa haraka. Angalia mwalimu wako haraka iwezekanavyo kujadili hali yako. Pamoja unaweza kuja na mpango wa kupata msaada unayohitaji.