Como calcular raiz quadrada de um numero impar

Narciso Busatto Algoritmo das Raizes Quadradas por Números Ímpares

3 󰁒AI󰁚 󰁑󰁕AD󰁒ADA 󰁐󰁏󰁒 󰁎󰃚󰁍E󰁒󰁏󰁓 󰃍󰁍󰁐A󰁒E󰁓 󰁏󰁢󰁳󰁥󰁲󰁶󰁥 󰁯 󰁱󰁵󰁥 󰁡󰁣󰁯󰁮󰁴󰁥󰁣󰁥 󰁱󰁵󰁡󰁮󰁤󰁯 󰁳󰁯󰁭󰁡󰁭󰁯󰁳 󰁯󰁳 󰁮 󰁰󰁲󰁩󰁭󰁥󰁩󰁲󰁯󰁳 󰁴󰁥󰁲󰁭󰁯󰁳 󰃭󰁭󰁰󰁡󰁲󰁥󰁳 󰁰󰁯󰁳󰁩󰁴󰁩󰁶󰁯󰁳.

 󰀽 󰀱

 󰀽 󰀱

 󰀽 󰀲

 󰀽 󰀱󰀫󰀳 󰀽 󰀴

 󰀽 󰀳

 󰀽 󰀱󰀫󰀳󰀫󰀵 󰀽 󰀹

 󰀽 󰀴

 󰀽 󰀱 󰀫󰀳 󰀫󰀵 󰀫󰀷 󰀽 󰀱󰀶

 ... ...

 󰀽 

 󰀽󰀿

 A󰁰󰁥󰁮󰁡󰁳 󰁰󰁥󰁬󰁡 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰃧󰃣󰁯, 󰁮󰁯󰁴󰁡󰀭󰁳󰁥 󰁱󰁵󰁥





 󰀽 󰂲

 󰁖󰁡󰁭󰁯󰁳 󰁤󰁥󰁭󰁯󰁮󰁳󰁴󰁲󰁡󰁲: 󰁌󰁥󰁭󰁡 1: A 󰁳󰁯󰁭󰁡 󰁤󰁯󰁳



 󰁰󰁲󰁩󰁭󰁥󰁩󰁲󰁯󰁳 󰃭󰁭󰁰󰁡󰁲󰁥󰁳 󰁰󰁯󰁳󰁩󰁴󰁩󰁶󰁯󰁳 󰃩

󰂲

 D󰁥󰁭󰁯󰁮󰁳󰁴󰁲󰁡󰃧󰃣󰁯: 󰁯󰁢󰁳󰁥󰁲󰁶󰁥 󰁱󰁵󰁥 󰁯󰁳 󰁮󰃺󰁭󰁥󰁲󰁯󰁳 󰃭󰁭󰁰󰁡󰁲󰁥󰁳 󰁰󰁯󰁳󰁩󰁴󰁩󰁶󰁯󰁳 󰁦󰁯󰁲󰁭󰁡󰁭, 󰁮󰁡 󰁳󰁵󰁡 󰁤󰁥󰁶󰁩󰁤󰁡 󰁯󰁲󰁤󰁥󰁭, 󰁵󰁭󰁡 󰁐.A. 󰁤󰁥 󰁲󰁡󰁺󰃣󰁯 󰁩󰁧󰁵󰁡󰁬 󰁡

󰀲

. A󰁳󰁳󰁩󰁭, 󰁴󰁥󰁭󰁯󰁳:

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

 󰀽 󰀱󰀫󰀳󰀫󰀵󰀫⋯󰀫󰀲 −󰀱

 󰁓󰁡󰁢󰁥󰁮󰁤󰁯 󰁱󰁵󰁥 󰁡 󰁳󰁯󰁭󰁡 󰁤󰁯󰁳



 󰁰󰁲󰁩󰁭󰁥󰁩󰁲󰁯󰁳 󰁴󰁥󰁲󰁭󰁯󰁳 󰁤󰁥 󰁵󰁭󰁡 󰁐.A. 󰃩 󰁤󰁡󰁤󰁡 󰁰󰁯󰁲

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

 󰀽 



 󰀫

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󰀮󰀲

 󰁔󰁥󰁭󰁯󰁳 󰁱󰁵󰁥:

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

 󰀽 󰀱 󰀫󰀲 −󰀱󰀮󰀲 󰀽 󰂲

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 A󰁌G󰁏󰁒I󰁔󰁍󰁏 DA 󰁒AI󰁚 󰁑󰁕AD󰁒ADA 󰁐󰁏󰁒 󰁎󰃚󰁍E󰁒󰁏󰁓 󰃍󰁍󰁐A󰁒E󰁓 󰁐󰁡󰁲󰁡 󰁳󰁥 󰁯󰁢󰁴󰁥󰁲 󰁡 󰁲󰁡󰁩󰁺 󰁱󰁵󰁡󰁤󰁲󰁡󰁤󰁡 󰁤󰁥 󰁵󰁭 󰁮󰃺󰁭󰁥󰁲󰁯, 󰁢󰁡󰁳󰁴󰁡 󰁲󰁥󰁡󰁬󰁩󰁺󰁡󰁲 󰁳󰁵󰁣󰁥󰁳󰁳󰁩󰁶󰁡󰁭󰁥󰁮󰁴󰁥 󰁡 󰁳󰁵󰁢󰁴󰁲󰁡󰃧󰃣󰁯 󰁤󰁯󰁳 󰁮󰃺󰁭󰁥󰁲󰁯󰁳 󰃭󰁭󰁰󰁡󰁲󰁥󰁳 󰁡󰁴󰃩 󰁱󰁵󰁥 󰁯 󰁶󰁡󰁬󰁯󰁲 0 󰁳󰁥󰁪󰁡 󰁯󰁢󰁴󰁩󰁤󰁯. E󰁭 󰁣󰁡󰁳󰁯 󰁰󰁯󰁳󰁩󰁴󰁩󰁶󰁯, 󰁡 󰁲󰁡󰁩󰁺 󰃩 󰁯 󰁮󰃺󰁭󰁥󰁲󰁯 󰁤󰁥 󰁳󰁵󰁢󰁴󰁲󰁡󰃧󰃵󰁥󰁳 󰁲󰁥󰁡󰁬󰁩󰁺󰁡󰁤󰁡󰁳. E󰁸󰁥󰁭󰁰󰁬󰁯:

√ 󰀹 󰀽󰀿

 󰁔󰁥󰁭󰁯󰁳 󰁡󰁳 󰁳󰁵󰁢󰁴󰁲󰁡󰃧󰃵󰁥󰁳 󰁥󰁭 󰁯󰁲󰁤󰁥󰁭: 9 󰀭 1 8 󰀭 3 5 󰀭 5 0 󰁏󰁢󰁳󰁥󰁲󰁶󰁥 󰁱󰁵󰁥 󰁡 󰁳󰁵󰁢󰁴󰁲󰁡󰃧󰃣󰁯 󰁳󰁵󰁣󰁥󰁳󰁳󰁩󰁶󰁡 󰁲󰁥󰁳󰁵󰁬󰁴󰁯󰁵 󰁥󰁭

󰀰

 (󰁺󰁥󰁲󰁯), 󰁯󰁵 󰁳󰁥󰁪󰁡,

󰀹

 󰃩 󰁵󰁭 󰁱󰁵󰁡󰁤󰁲󰁡󰁤󰁯 󰁰󰁥󰁲󰁦󰁥󰁩󰁴󰁯 󰁥 󰁳󰁵󰁡 󰁲󰁡󰁩󰁺 󰃩 󰁯 󰁮󰃺󰁭󰁥󰁲󰁯 󰁤󰁥 󰁳󰁵󰁢󰁴󰁲󰁡󰃧󰃵󰁥󰁳 󰁲󰁥󰁡󰁬󰁩󰁺󰁡󰁤󰁡󰁳:

√ 󰀹 󰀽 󰀳

 9 󰀭 1 8 󰀭 3 5 󰀭 5 0

Narciso Busatto Algoritmo das Raizes Quadradas por Números Ímpares

I󰁳󰁳󰁯 󰃩 󰁶󰃡󰁬󰁩󰁤󰁯 󰁰󰁡󰁲󰁡 󰁱󰁵󰁡󰁬󰁱󰁵󰁥󰁲 󰁶󰁡󰁬󰁯󰁲:

√ 󰀱󰀶 󰀽 󰀴 󰀴 󰃧󰃵

 16 󰀭 1 15 󰀭 3 12 󰀭 5 7 󰀭 7 0 A󰁬󰁧󰁵󰁭󰁡󰁳 󰁰󰁥󰁳󰁳󰁯󰁡󰁳 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁭 󰁯 󰁰󰁲󰁯󰁣󰁥󰁳󰁳󰁯 󰁥 󰁦󰁡󰁺󰁥󰁭 󰁯 󰁳󰁥󰁧󰁵󰁩󰁮󰁴󰁥 󰁱󰁵󰁥󰁳󰁴󰁩󰁯󰁮󰁡󰁭󰁥󰁮󰁴󰁯: 󰁏 󰁰󰁲󰁯󰁣󰁥󰁤󰁩󰁭󰁥󰁮󰁴󰁯 󰃩 󰁦󰃡󰁣󰁩󰁬 󰁰󰁡󰁲󰁡 󰁮󰃺󰁭󰁥󰁲󰁯󰁳 󰁰󰁥󰁱󰁵󰁥󰁮󰁯󰁳, 󰁭󰁡󰁳 󰁪󰃡 󰁰󰁡󰁲󰁡 󰁮󰃺󰁭󰁥󰁲󰁯󰁳 󰁭󰁡󰁩󰁯󰁲󰁥󰁳, 󰁡 󰁱󰁵󰁡󰁮󰁴󰁩󰁤󰁡󰁤󰁥 󰁤󰁥 󰁳󰁵󰁢󰁴󰁲󰁡󰃧󰃵󰁥󰁳 󰃩 󰁣󰁯󰁭󰁰󰁬󰁥󰁴󰁡󰁭󰁥󰁮󰁴󰁥 󰁥󰁸󰁡󰁵󰁳󰁴󰁩󰁶󰁡. E󰁭 󰁲󰁥󰁳󰁰󰁯󰁳󰁴󰁡 󰁡 󰁥󰁳󰁳󰁡 󰁱󰁵󰁥󰁳󰁴󰃣󰁯, 󰁯 󰁡󰁬󰁧󰁯󰁲󰁩󰁴󰁭󰁯 󰁰󰁯󰁳󰁳󰁵󰁩 󰁵󰁭 󰁭󰃩󰁴󰁯󰁤󰁯 󰁩󰁮󰁴󰁥󰁲󰁥󰁳󰁳󰁥, 󰁱󰁵󰁥 󰁰󰁯󰁤󰁥 󰁳󰁥󰁲 󰁣󰁯󰁭󰁰󰁲󰁥󰁥󰁮󰁤󰁩󰁤󰁯 󰁡󰁢󰁡󰁩󰁸󰁯: E󰁸󰁥󰁭󰁰󰁬󰁯: C󰁡󰁬󰁣󰁵󰁬󰁥

√ 󰀵󰀲󰀹

󰁁󰁬󰁧󰁯󰁲󰁩󰁴󰁭󰁯󰀺

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󰁐󰁲󰁩󰁭󰁥󰁩󰁲󰁡󰁭󰁥󰁮󰁴󰁥, 󰁳󰁥󰁰󰁡󰁲󰁥 󰁯 󰁮󰃺󰁭󰁥󰁲󰁯 󰁥󰁭 󰁰󰁡󰁲󰁥󰁳, 󰁤󰁡 󰁤󰁩󰁲󰁥󰁩󰁴󰁡 󰁰󰁡󰁲󰁡 󰁡 󰁥󰁳󰁱󰁵󰁥󰁲󰁤󰁡

󰀵 󰀲󰀹

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C󰁯󰁭󰁥󰁣󰁥 󰁡 󰁳󰁵󰁢󰁴󰁲󰁡󰁩󰁲 󰁯 󰁰󰁡󰁲 󰁭󰁡󰁩󰁳 󰁡 󰁥󰁳󰁱󰁵󰁥󰁲󰁤󰁡. 5 29 󰀭 1 4 󰀭 3 1 J󰃡 󰁥󰁳󰁰󰁥󰁲󰃡󰁶󰁡󰁭󰁯󰁳 󰁱󰁵󰁥 󰁡 󰁳󰁵󰁢󰁴󰁲󰁡󰃧󰃣󰁯 󰁮󰃣󰁯 󰁣󰁨󰁥󰁧󰁡󰁲󰁩󰁡 󰁡 0, 󰁰󰁯󰁩󰁳 5 󰁮󰃣󰁯 󰃩 󰁵󰁭 󰁱󰁵󰁡󰁤󰁲󰁡󰁤󰁯 󰁰󰁥󰁲󰁦󰁥󰁩󰁴󰁯.

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D󰁥󰁳󰃧󰁡 󰁯 󰁰󰁲󰃳󰁸󰁩󰁭󰁯 󰁰󰁡󰁲 5 29 󰀭 1 4 󰀭 3 1 29 󰁎󰁯󰁴󰁥 󰁱󰁵󰁥 󰁦󰁯󰁲󰁭󰁡󰁭󰁯󰁳 󰁯 󰁮󰃺󰁭󰁥󰁲󰁯 129. A󰁴󰁥󰁮󰃧󰃣󰁯 󰁡 󰁥󰁳󰁳󰁥 󰁰󰁡󰁳󰁳󰁯!!!

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󰁔󰁯󰁭󰁥 󰁯 󰃺󰁬󰁴󰁩󰁭󰁯 󰃭󰁭󰁰󰁡󰁲 󰁵󰁴󰁩󰁬󰁩󰁺󰁡󰁤󰁯, 󰁳󰁯󰁭󰁥 󰁭󰁡󰁩󰁳 󰁵󰁭 󰁥 󰁣󰁯󰁬󰁯󰁱󰁵󰁥󰀭󰁯 󰁣󰁯󰁭󰁯 󰁤󰁥󰁺󰁥󰁮󰁡 󰁤󰁯 󰁰󰁲󰃳󰁸󰁩󰁭󰁯 󰃭󰁭󰁰󰁡󰁲 󰁡 󰁳󰁥󰁲 󰁵󰁴󰁩󰁬󰁩󰁺󰁡󰁤󰁯. 5 29 󰀭 1 4 󰀭 3 129 41 3+1=4

Narciso Busatto Algoritmo das Raizes Quadradas por Números Ímpares

󰁎󰃣󰁯 󰁳󰁥 󰁥󰁳󰁱󰁵󰁥󰃧󰁡 󰁤󰁥 󰁱󰁵󰁥 󰁯 󰁰󰁲󰃳󰁸󰁩󰁭󰁯 󰁥󰁬󰁥󰁭󰁥󰁮󰁴󰁯 󰃩 󰁵󰁭 󰁮󰃺󰁭󰁥󰁲󰁯 󰃭󰁭󰁰󰁡󰁲. C󰁯󰁭󰁯 󰁯 4, 󰁡󰁯 󰁶󰁩󰁲󰁡󰁲 󰁵󰁭󰁡 󰁤󰁥󰁺󰁥󰁮󰁡, 󰁧󰁥󰁲󰁡 󰁯 󰁥󰁬󰁥󰁭󰁥󰁮󰁴󰁯 40, 󰁵󰁴󰁩󰁬󰁩󰁺󰁡󰁭󰁯󰁳 41 󰁱󰁵󰁥 󰃩 󰁯 󰁰󰁲󰃳󰁸󰁩󰁭󰁯 󰃭󰁭󰁰󰁡󰁲.

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C󰁯󰁮󰁴󰁩󰁮󰁵󰁥 󰁡 󰁳󰁵󰁢󰁴󰁲󰁡󰃧󰃣󰁯 5 29 󰀭 1 4 󰀭 3 129 󰀭 41 88 󰀭 43 45 󰀭 45 0

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C󰁯󰁮󰁴󰁥 󰁯 󰁮󰃺󰁭󰁥󰁲󰁯 󰁤󰁥 󰁳󰁵󰁢󰁴󰁲󰁡󰃧󰃵󰁥󰁳 󰁎󰁯󰁴󰁥 󰁱󰁵󰁥 󰁲󰁥󰁡󰁬󰁩󰁺󰁡󰁭󰁯󰁳 󰁰󰁲󰁩󰁭󰁥󰁩󰁲󰁡󰁭󰁥󰁮󰁴󰁥 2 󰁳󰁵󰁢󰁴󰁲󰁡󰃧󰃵󰁥󰁳. D󰁥󰁰󰁯󰁩󰁳, 󰁡󰁰󰃳󰁳 󰁤󰁥󰁳󰁣󰁥󰁲 󰁯 󰁮󰁯󰁶󰁯 󰁰󰁡󰁲, 󰁲󰁥󰁡󰁬󰁩󰁺󰁡󰁭󰁯󰁳 3 󰁳󰁵󰁢󰁴󰁲󰁡󰃧󰃵󰁥󰁳. 󰁌󰁯󰁧󰁯

√ 󰀵󰀲󰀹 󰀽 󰀲󰀳

 5 29 󰀭 1 4 󰀭 3 129 󰀭 41 88 󰀭 43 45 󰀭 45 0 󰁖A󰁎󰁔AGE󰁎󰁓 󰁘 DE󰁓󰁖A󰁎󰁔AGE󰁎󰁓 󰁖A󰁎󰁔AGE󰁎󰁓 D󰁏 A󰁌G󰁏󰁒I󰁔󰁍󰁏:

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󰁎󰃣󰁯 󰃩 󰁮󰁥󰁣󰁥󰁳󰁳󰃡󰁲󰁩󰁯 󰁦󰁡󰁴󰁯󰁲󰁡󰁲 󰁯 󰁥󰁬󰁥󰁭󰁥󰁮󰁴󰁯 󰁥󰁭 󰁱󰁵󰁥󰁳󰁴󰃣󰁯.

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󰁐󰁯󰁤󰁥󰀭󰁳󰁥 󰁯󰁢󰁴󰁥󰁲 󰁡 󰁲󰁡󰁩󰁺 󰁱󰁵󰁡󰁤󰁲󰁡󰁤󰁡 󰁤󰁥 󰁱󰁵󰁡󰁬󰁱󰁵󰁥󰁲 󰁮󰃺󰁭󰁥󰁲󰁯, 󰁳󰁥󰁭 󰁮󰁥󰁣󰁥󰁳󰁳󰁩󰁤󰁡󰁤󰁥 󰁤󰁥 󰁴󰁥󰁮󰁴󰁡󰁴󰁩󰁶󰁡󰁳, 󰁯󰁢󰁴󰁥󰁮󰁤󰁯󰀭󰁳󰁥 󰁡 󰁥󰁳󰁴󰁩󰁭󰁡󰁴󰁩󰁶󰁡 󰁤󰁥 󰁲󰁡󰃭󰁺󰁥󰁳 󰁱󰁵󰁡󰁤󰁲󰁡󰁤󰁡󰁳 󰁤󰁩󰁲󰁥󰁴󰁡󰁭󰁥󰁮󰁴󰁥.

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󰁐󰁯󰁳󰁳󰁩󰁢󰁩󰁬󰁩󰁤󰁡󰁤󰁥 󰁤󰁥 󰁣󰃡󰁬󰁣󰁵󰁬󰁯 󰁤󰁩󰁲󰁥󰁴󰁯 󰁤󰁥 󰁮󰃺󰁭󰁥󰁲󰁯󰁳 󰁤󰁥󰁣󰁩󰁭󰁡󰁩󰁳.

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󰁍󰁡󰁩󰁳 󰁩󰁮󰁴󰁥󰁲󰁥󰁳󰁳󰁡󰁮󰁴󰁥 󰁰󰁡󰁲󰁡 󰁡󰁬󰁧󰁯󰁲󰁩󰁴󰁭󰁯󰁳 󰁣󰁯󰁭󰁰󰁵󰁴󰁡󰁣󰁩󰁯󰁮󰁡󰁩󰁳 󰁮󰁡 󰁢󰁵󰁳󰁣󰁡 󰁤󰁥 󰁭󰁡󰁩󰁳 󰁡󰁬󰁧󰁡󰁲󰁩󰁳󰁭󰁯 󰁳󰁩󰁧󰁮󰁩󰁦󰁩󰁣󰁡󰁴󰁩󰁶󰁯󰁳 DE󰁓󰁖A󰁎󰁔AGE󰁎󰁓 D󰁏 A󰁌G󰁏󰁒I󰁔󰁍󰁏:

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󰁑󰁵󰁡󰁮󰁴󰁩󰁤󰁡󰁤󰁥 󰁤󰁥 󰁳󰁵󰁢󰁴󰁲󰁡󰃧󰃵󰁥󰁳 󰁮󰁥󰁣󰁥󰁳󰁳󰃡󰁲󰁩󰁡󰁳. 2 󰁳󰁵󰁢󰁴󰁲󰁡󰃧󰃵󰁥󰁳 3 󰁳󰁵󰁢󰁴󰁲󰁡󰃧󰃵󰁥󰁳