Mene ne square tushen?

Daga cikin sa na ilimi, wanda shi ne wata ãyã daga rubuce-rubuce a cikin na farko wuri ne da haruffa. Next, a cikin wannan "gagarumin" kashi ne Bugu da kari-multiplication basira da kuma m zuwa gare su, amma kuma baya da ma'anar, ilmin lissafi subtraction, division. Darussa a cikin m yara makaranta basira, bauta da aminci rana da dare: TV, jaridar, SMS daftari. Kuma a ko'ina, muna karanta, rubuta, view, ƙara, ɗebewa, ninka. Kuma, gaya mani, sau nawa kuke da zuwa rayuwa, cire tushen, fãce kamar yadda a cikin kasar? Alal misali, irin wannan nishadi da aiki, kamar, da square tushen na lamba 12345 ... Akwai rayuwa a cikin tsohon kare? Ƙware? Na'am, akwai kome sauki! Ina kalkuleta ... Kuma ba tare da shi, hannu da hannu, kadan?

Da farko, bari mu saka abin da shi ne - da square tushen na lamba. Kullum magana, "to cire square tushen na lamba" yana nufin a yi ilmin lissafi aiki gaban exponentiation - shi ke da ku da kuma hadin kai na hamayya da juna a rayuwar aikace-aikace. Exponentiation, bari mu ce, wata square, ne multiplication da dama da kanta, watau, kamar yadda aka koyar a makaranta, X * X = A ko wasu shigarwar x2 = A, da kuma kalmomi - "X Squared ne daidai A". Sai kishiya matsala ne: square tushen na A, X ne a yawan da ake gina a cikin square da aka daidaita A.

square tushen

Daga mai makaranta hanya na ilmin lissafi da hanyoyin da aka sani sarrafa kwamfuta "a cikin shafi" cewa taimako yin wani lissafin amfani da farko hudu arithmetical ayyukan. Alas ... Don Square, kuma ba kawai square ƙarshen waɗancan lissafi mai tsauri ba wanzu. Kuma a cikin wannan harka, kamar yadda square tushen ba tare da wani kalkuleta? Bisa ga definition of wani square tushen fitarwa - shi wajibi ne don zaɓar sakamakon darajar zaluncin 'yan lambobi wanda square halarci tamanin da radicand. Wannan duk! Ba su da lokacin da za a wuce awa daya ko biyu, kamar yadda yake yiwuwa yin lissafi, ta amfani da sanannun hanya na multiplication a cikin "shafi" na wani square tushen. Idan kun kasance dadi isa ya yi kamar wata minti. Ko ba sosai m mai amfani da kalkaleta ko PC sa shi a daya fadi karkata guda - ci gaba.

Amma tsanani, da square tushen ne sau da yawa yi amfani da hanyar da "manyan bindigogi cokula masu yatsotsi": da farko dauki lamba wanda square, wajen yayi dace da radicals. Yana da kyau idan "mu square" kadan kasa da wannan magana. Sa'an nan, daidaita yawan nasu ikon, fahimtar, misali, ta tara da biyu, da kuma ... sake Squared. Idan sakamakon ya fi yawan kasa da tushen nasarar gyara asali lambar da aka hankali gabatowa ta "takwaransa" a karkashin tushen. Kamar yadda ka gani - ba kalkuleta, kawai da ikon da za a gani "a cikin wani shafi". Hakika, akwai mutane da yawa kimiyya da muhawwara da kuma gyara lissafi mai tsauri ga kwamfuta square Tushen, amma ga "gidan amfani" ci sama ba 100% amincewa a sakamakon.

Oh, na kusan manta tabbatar ta ƙara rubuce-rubuce, lissafi da square tushen na baya kayyade yawan 12345. Make a mataki-mataki:

1. Ka lamirinsu, X = 100. Mun lissafta: X * X = 10,000 diraya a tsawo - sakamakon shi ne kasa da 12345.

2. Ka yi kokarin ma lamirinsu, X = 120. Sa'an nan: X * X = 14400.I sake tare da diraya domin - sakamakon fiye da 12345.

3. The sama samu "cokali mai yatsu" na 100 da kuma 120. Zabi wani sabon lamba - 110 da 115. Mun sami, bi da bi, 12100 da 13225 - cokali mai yatsu Narrows.

4. Ka yi kokarin "bazuwar" X = 111. * Ka X = X 12321. Wannan lambar ne kusa isa ga 12345. A daidai da bukata daidaito "shige" iya ci gaba ko daina a kan sakamakon da muka samu. Shi ke nan. Kamar yadda shi wa'adi da - kome ne mai sauqi qwarai da kuma ba tare da wani kalkuleta.

Quite a bit na tarihi ...

Sun buga a kan ra'ayin don amfani da square tushen har yanzu Pythagoreans, makaranta ƴan kuma mabiya Pythagoras, 800 BC sa'an nan "gudu" saboda sabon binciken a fagen lambobi. Kuma ina da ya zo daga?

1. A maganin matsalar da cire tushen, ya bada sakamakon a cikin nau'i na wani sabon aji na lambobin. Suka kira m, cewa shi ne ya ce, "m" saboda su ba su rubuta cikakken lambar. A mafi classic misali na irin wannan - square tushen na 2. Wannan harka yayi dace da lissafi na diagonal na wani square da wani gefen daidaita 1 - wato, rinjayar da makaranta na Pythagoras. Sai ya juya daga cewa a alwatika da sosai musamman size of guda gefe, da hypotenuse wata size cewa an bayyana ta da wani yawan, a cikin abin da "babu karshen." Saboda haka a cikin ilmin lissafi bayyana m lambobi.

2. An sani cewa kõfatansu a kan duwatsu matsala fara. Sai ya juya daga cewa wannan ilmin lissafi aiki ya ƙunshi wani abin zamba - shan square tushe, ba mu san square na lamba, tabbatacce ko korau, shi ne m magana. Wannan rashin tabbas, da biyu sakamakon guda aiki, da kuma rubuce.

A binciken da hade da wannan sabon abu damuwa ya shugabanci a ilmin lissafi, da ake kira da ka'idar hadaddun m, wanda shi ne na girma m muhimmanci a ilmin lissafi kimiyyar lissafi.

Abin mamaki, nadi na tushen - a - amfani a cikin "Universal ilmin lissafi" ne guda ubiquitous Newton, da kuma na zamani look daidai da rikodin da tushen da aka sani tun 1690 daga littafin Bafaranshen Rolle "Shiryar aljabara".