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9.1E: Mazoezi

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    177453

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    Mazoezi hufanya kamili

    Rahisisha maneno na Mizizi ya Mraba

    Katika mazoezi yafuatayo, kurahisisha.

    Mfano\(\PageIndex{34}\)

    \(\sqrt{36}\)

    Jibu

    6

    Mfano\(\PageIndex{35}\)

    \(\sqrt{4}\)

    Mfano\(\PageIndex{36}\)

    \(\sqrt{64}\)

    Jibu

    8

    Mfano\(\PageIndex{37}\)

    \(\sqrt{169}\)

    Mfano\(\PageIndex{38}\)

    \(\sqrt{9}\)

    Jibu

    3

    Mfano\(\PageIndex{39}\)

    \(\sqrt{16}\)

    Mfano\(\PageIndex{40}\)

    \(\sqrt{100}\)

    Jibu

    10

    Mfano\(\PageIndex{41}\)

    \(\sqrt{144}\)

    Mfano\(\PageIndex{42}\)

    \(−\sqrt{4}\)

    Jibu

    -2

    Mfano\(\PageIndex{43}\)

    \(−\sqrt{100}\)

    Mfano\(\PageIndex{44}\)

    \(−\sqrt{1}\)

    Jibu

    -1

    Mfano\(\PageIndex{45}\)

    \(−\sqrt{121}\)

    Mfano\(\PageIndex{46}\)

    \(\sqrt{−121}\)

    Jibu

    si idadi halisi

    Mfano\(\PageIndex{47}\)

    \(\sqrt{−36}\)

    Mfano\(\PageIndex{48}\)

    \(\sqrt{−9}\)

    Jibu

    si idadi halisi

    Mfano\(\PageIndex{49}\)

    \(\sqrt{−49}\)

    Mfano\(\PageIndex{50}\)

    \(\sqrt{9+16}\)

    Jibu

    5

    Mfano\(\PageIndex{51}\)

    \(\sqrt{25+144}\)

    Mfano\(\PageIndex{52}\)

    \(\sqrt{9}+\sqrt{16}\)

    Jibu

    7

    Mfano\(\PageIndex{53}\)

    \(\sqrt{25}+\sqrt{144}\)

    Tathmini Mizizi ya Mraba

    Katika mazoezi yafuatayo, tathmini kila mizizi ya mraba kati ya namba mbili za mfululizo.

    Mfano\(\PageIndex{54}\)

    \(\sqrt{70}\)

    Jibu

    \(8<\sqrt{70}<9\)

    Mfano\(\PageIndex{55}\)

    \(\sqrt{55}\)

    Mfano\(\PageIndex{56}\)

    \(\sqrt{200}\)

    Jibu

    \(14<\sqrt{200}<15\)

    Mfano\(\PageIndex{57}\)

    \(\sqrt{172}\)

    Mizizi ya Mraba

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

    Mfano\(\PageIndex{58}\)

    \(\sqrt{19}\)

    Jibu

    4.36

    Mfano\(\PageIndex{59}\)

    \(\sqrt{21}\)

    Mfano\(\PageIndex{60}\)

    \(\sqrt{53}\)

    Jibu

    7.28

    Mfano\(\PageIndex{61}\)

    \(\sqrt{47}\)

    Punguza maneno ya kutofautiana na Mizizi ya Mraba

    Katika mazoezi yafuatayo, kurahisisha.

    Mfano\(\PageIndex{62}\)

    \(\sqrt{y^2}\)

    Jibu

    y

    Mfano\(\PageIndex{63}\)

    \(\sqrt{b^2}\)

    Mfano\(\PageIndex{64}\)

    \(\sqrt{a^{14}}\)

    Jibu

    \(a^7\)

    Mfano\(\PageIndex{65}\)

    \(\sqrt{w^{24}}\)

    Mfano\(\PageIndex{66}\)

    \(\sqrt{49x^2}\)

    Jibu

    \(7x\)

    Mfano\(\PageIndex{67}\)

    \(\sqrt{100y^2}\)

    Mfano\(\PageIndex{68}\)

    \(\sqrt{121m^{20}}\)

    Jibu

    \(11m^{10}\)

    Mfano\(\PageIndex{69}\)

    \(25h^{44}\)

    Mfano\(\PageIndex{70}\)

    \(\sqrt{81x^{36}}\)

    Jibu

    \(9x^{18}\)

    Mfano\(\PageIndex{71}\)

    \(\sqrt{144z^{84}}\)

    Mfano\(\PageIndex{72}\)

    \(−\sqrt{81x^{18}}\)

    Jibu

    \(−9x^9\)

    Mfano\(\PageIndex{73}\)

    \(−\sqrt{100m^{32}}\)

    Mfano\(\PageIndex{74}\)

    \(−\sqrt{64a^2}\)

    Jibu

    \(−8a\)

    Mfano\(\PageIndex{75}\)

    \(−\sqrt{25x^2}\)

    Mfano\(\PageIndex{76}\)

    \(\sqrt{144x^{2}y^{2}}\)

    Jibu

    \(12xy\)

    Mfano\(\PageIndex{77}\)

    \(\sqrt{196a^{2}b^{2}}\)

    Mfano\(\PageIndex{78}\)

    \(\sqrt{169w^{8}y^{10}}\)

    Jibu

    \(13w^{4}y^{5}\)

    Mfano\(\PageIndex{79}\)

    \(\sqrt{81p^{24}q^{6}}\)

    Mfano\(\PageIndex{80}\)

    \(\sqrt{9c^{8}d^{12}}\)

    Jibu

    \(3c^{4}d^{6}\)

    Mfano\(\PageIndex{81}\)

    \(\sqrt{36r^{6}s^{20}}\)

    kila siku Math

    Mfano\(\PageIndex{82}\)

    Mapambo Denise anataka kuwa na msukumo wa mraba wa matofali ya designer katika oga yake mpya. Anaweza kumudu kununua sentimita za mraba 625 za matofali ya designer. Je, upande wa msukumo unaweza kuwa muda gani?

    Jibu

    Sentimita 25

    Mfano\(\PageIndex{83}\)

    Mapambo Morris anataka kuwa na mosaic mraba inlaid katika patio yake mpya. Bajeti yake inaruhusu tiles 2025 mraba inch. Je, upande wa mosaic unaweza kuwa muda gani?

    Mazoezi ya kuandika

    Mfano\(\PageIndex{84}\)

    Kwa nini hakuna idadi halisi sawa na\(\sqrt{−64}\)?

    Jibu

    Majibu yatatofautiana.

    Mfano\(\PageIndex{85}\)

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

    Self Check

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

    Jedwali hili lina nguzo nne na safu tano. Nguzo zimeandikwa, “Ninaweza...,” “Kwa bahati mbaya,” “Kwa msaada fulani,” na “Hapana - Siipati!” Chini ya “Ninaweza...,” safu ni, “kurahisisha maneno na mizizi ya mraba.,” “makadirio ya mizizi ya mraba.,” “mizizi ya mraba takriban.,” na “4) kurahisisha maneno ya kutofautiana na mizizi ya mraba.” Safu nyingine zote chini ya nguzo tofauti ni tupu.

    ⓑ Kwa kiwango cha 1—10, ungewezaje kupima ujuzi wako wa sehemu hii kwa kuzingatia majibu yako kwenye orodha? Unawezaje kuboresha hii?