Back to makaranta. tushen Bugu da kari

Yau zamani lantarki kwakwalwa kirga cikin square tushen da yawan ba mai wuya aiki. Alal misali, √2704 = 52, wannan shi ne ka lissafi wani kalkuleta. Sa'a, da kalkaleta ne ba kawai a kan Windows, amma kuma a cikin talakawa, har ma ya fi unpretentious, waya. Gaskiya idan ba zato ba tsammani (a low yiwuwa, ƙidãyar wanda, ba zato ba tsammani, ya hada da Bugu da kari na tushen), za ka sami kanka ba tare da samuwa kudi, sa'an nan, alas, dole sunã dõgara a kan tarar da kwakwalwarmu.

Horar da hankali ne ba sa. Musamman ga wadanda suka ba haka sau da yawa aiki tare da lambobi, kuma ma fiye da haka tare da asalinsu. Bugu da kari kuma subtraction ne tushen - mai kyau motsa jiki ga hankali gundura. Kuma zan nuna maka Mataki-mataki Bugu da kari na asalinsu. Zancen Misalai iya zama kamar haka.

A lissafi da cewa bukatar a Sauki:

√2 + 3√48-4 × √27 + √128

Wannan shi ne wani m magana. Domin ya rage wuya da shi wajibi ne don kawo duk radicands zuwa janar form. Mun kada mataki-mataki:

A farko lambar ba za a iya Sauki. Mu juya ga karo na biyu.

3√48 decompose a ninkãwa 48: 48 = 2 × 24 ko 48 × 16 = 3. A square tushen na 24 ne ba da wani lamba, Ina nufin wani fractional saura. Tun da muna bukatar da ainihin darajar, m tushen ba su dace. A square tushen na 16 ne hudu, don yin shi daga karkashin tushen alama. Mun samu 4 × 3 × √3 = 12 × √3

A gaba sanarwa mu ne korau, watau, aka rubuta tare da wani debe -4 × √ (27.) Yada 27 ninkãwa. Mun samu 27 × 3 = 9. Ba mu yi amfani da fractional ninkãwa saboda kasarun adadi yin lissafi da square tushen daga cikin hadaddun. 9 dauki fita daga karkashin farantin, Ina nufin Mun ƙididdige square tushen. Mun samu da wadannan magana: -4 × 3 × √3 = -12 × √3

Next lokaci √128 lissafi da kashi cewa za a iya dauka fita daga karkashin tushen. 128 = 64 × 2, inda √64 = 8. Idan ba za ka iya kwatanta shi zai kasance da sauki wannan magana a matsayin: √128 = √ (8 ^ 2 × 2)

Mun yi tasiri a magana Sauki sharuddan:

√2 + 12 × √3-12 × √3 + 8 × √2

Yanzu muna ƙara sama da adadin guda radicals. Ba za ka iya ƙara ko muka ɗebe magana daga daban-daban radicals. tushen Bugu da kari bukatar yarda da wannan mulkin.

Mun samu wadannan amsa:

√2 + 12√3-12√3 + 8√2 = 9√2

√2 = 1 × √2 - fatan cewa a aljabara yanke shawarar ƙetare irin abubuwa ba za su zama labarai zuwa gare ku.

Maganganu za a iya wakilta ba kawai ta square tushen, amma kuma tare da wani cubic tushen ko n-hydrochloric har.

Bugu da kari kuma subtraction Tushen tare da daban-daban exponents, amma tare da m radicand, shi ne kamar haka:

Idan muna da wani magana kamar √a + ∛b + ∜b, za mu iya rage wuya da wannan magana kamar haka:

∛b + ∜b = 12 × √b4 + 12 × √b3

12√b4 + 12 × √b3 = 12 × √b4 + b3

Mun kawo biyu irin mambobi zuwa wani na kowa nuna alama daga cikin tushen. A nan mun yi amfani da tushen da dukiya, wanda ya karanta kamar haka: idan yawan digiri na m magana da yawan tushen index yawaita da wannan lambar, ta lissafi ya zauna canzawa.

Lura: da exponents kawai ƙara sama a lokacin da yawaita.

Ga wani misali inda yanzu cikin sharuddan da sulusi da murabba'i.

5√8-4 × √ (1/4) + √72-4 × √2

Za mu yanke shawara a kan matakai:

5√8 = 5 * 2√2 - mu yi daga tushen na retrievable.

- 4√ (1/4) = - 4 √1 / (√4) = - 4 * 1/2 = - 2

Idan tushen na jiki da aka wakilta wani sulusi da murabba'i, da sulusi da murabba'i ne ba wani ɓangare na wannan canji, idan square tushen da rara, kuma divisor. A sakamakon haka, mun samu daidaito da aka bayyana a sama.

√72-4√2 = √ (2 × 36) - 4√2 = 2√2

10√2 + 2√2-2 = 12√2-2

Saboda haka don samun amsa.

Babban abu a tuna cewa korau lambobin ba za a iya fita tushen tare da wani ko da exponent. Idan har digiri radicand ne, a'a, to da magana ne unsolvable.

Bugu da kari daga cikin tushen mai yiwuwa ne kawai a lokacin da daidaituwa da maganganu a cikin radicals saboda suna kama da sharuddan. Haka ya shafi bambanci.

Bugu da kari na Tazarar Tushen tare da daban-daban exponents yi ta kawo wa jimlar har na tushen na biyu sharuddan. Wannan dokar yana da irin wannan tasirin a matsayin rage zuwa hada a lokacin da ƙara, ko subtracting kasarun adadi.

Idan radicand yana da yawan tashe zuwa ikon wannan magana za a iya Sauki ta dauka cewa tushen tsakanin index da kuma har akwai wani hada.