Question

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Resolva e indique os termos: índice, radicando e radical de cada termo abaixo. Raiz cúbica

²√16=.
³√27=.
²√25=​

Answer 1

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$\huge\green{\boxed{\rm~~~\red{ A)}~\gray{\sqrt[2]{16}}~\pink{=}~\blue{ 4 }~~~}}$

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$\huge\green{\boxed{\rm~~~\red{ B)}~\gray{\sqrt[3]{27}}~\pink{=}~\blue{ 3 }~~~}}$

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$\huge\green{\boxed{\rm~~~\red{ C)}~\gray{\sqrt[2]{25}}~\pink{=}~\blue{ 5 }~~~}}$

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$\green{\rm\underline{EXPLICAC_{\!\!\!,}\tilde{A}O\ PASSO{-}A{-}PASSO\ \ \ }}$✍

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☺lá, como tens passado nestes tempos de quarentena⁉ E os estudos à distância, como vão⁉ Espero que bem❗ Acompanhe a resolução abaixo, feita através de algumas manipulações algébricas, e após o resultado você encontrará um link com mais informações sobre Potenciação e Radiciação que talvez te ajude com exercícios semelhantes no futuro. ✌

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☔ O radical é o próprio símbolo de raiz no termo. O índice é o grau da raiz, indicado na parte superior esquerda do radical. O radicando é o valor de dentro do radical, a base.

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Ⓐ$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad}}$✍

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$\Huge\gray{\boxed{\sf\blue{~~\sqrt[2]{16}~~}}}$

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$\LARGE\blue{\text{ \sf = 16^{\frac{1}{2}} }}$

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☔ Fatorando o 16 encontramos

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$\boxed{\sf\Large\blue{\begin{array}{cc|cl}&&&\sf\underline{~F~}\\&&&\\16&&&2\\&&&\\8&&&2\\&&&\\4&&&2\\&&&\\2&&&2\\&&&\\1&&&\gray{\boxed{\LARGE\blue{\sf 2^4}}}\\\end{array}}}$

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$\LARGE\blue{\text{ \sf = (2^4)^{\frac{1}{2}} }}$

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$\LARGE\blue{\text{ \sf = 2^{\frac{4 \cdot 1}{2}} }}$

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$\LARGE\blue{\text{ \sf = 2^{\frac{4}{2}} }}$

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$\LARGE\blue{\sf = 2^2 }$

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$\LARGE\blue{\sf = 4 }$

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$\huge\green{\boxed{\rm~~~\red{ A)}~\gray{\sqrt[2]{16}}~\pink{=}~\blue{ 4 }~~~}}$ ✅

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Ⓑ$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad}}$✍

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$\Huge\gray{\boxed{\sf\blue{~~\sqrt[3]{27}~~}}}$

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$\LARGE\blue{\text{ \sf = 27^{\frac{1}{3}} }}$

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☔ Fatorando o 27 encontramos

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$\boxed{\sf\Large\blue{\begin{array}{cc|cl}&&&\sf\underline{~F~}\\&&&\\27&&&3\\&&&\\9&&&3\\&&&\\3&&&3\\&&&\\1&&&\gray{\boxed{\LARGE\blue{\sf 3^3}}}\\\end{array}}}$

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$\LARGE\blue{\text{ \sf = (3^3)^{\frac{1}{3}} }}$

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$\LARGE\blue{\text{ \sf = 3^{\frac{3 \cdot 1}{3}} }}$

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$\LARGE\blue{\text{ \sf = 3^{\frac{3}{3}} }}$

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$\LARGE\blue{\sf = 3^1 }$

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$\LARGE\blue{\sf = 3 }$

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$\huge\green{\boxed{\rm~~~\red{ B)}~\gray{\sqrt[3]{27}}~\pink{=}~\blue{ 3 }~~~}}$ ✅

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Ⓒ$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad}}$✍

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$\Huge\gray{\boxed{\sf\blue{~~\sqrt[2]{25}~~}}}$

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$\LARGE\blue{\text{ \sf = 25^{\frac{1}{2}} }}$

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☔ Fatorando o 25 encontramos

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$\boxed{\sf\Large\blue{\begin{array}{cc|cl}&&&\sf\underline{~F~}\\&&&\\25&&&5\\&&&\\5&&&5\\&&&\\1&&&\gray{\boxed{\LARGE\blue{\sf 5^2}}}}\\\end{array}}$

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$\LARGE\blue{\text{ \sf = (5^2)^{\frac{1}{2}} }}$

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$\LARGE\blue{\text{ \sf = 5^{\frac{2 \cdot 1}{2}} }}$

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$\LARGE\blue{\text{ \sf = 5^{\frac{2}{2}} }}$

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$\LARGE\blue{\sf = 5^1 }$

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$\LARGE\blue{\sf = 5 }$

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$\huge\green{\boxed{\rm~~~\red{ C)}~\gray{\sqrt[2]{25}}~\pink{=}~\blue{ 5 }~~~}}$ ✅

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$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$

✈ Potenciação e Radiciação (https://brainly.com.br/tarefa/36120526)

$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad}}$✍

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$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$☁

☕ $\bf\Large\blue{Bons\ estudos.}$

($\orange{D\acute{u}vidas\ nos\ coment\acute{a}rios}$) ☄

$\bf\large\red{\underline{\qquad \qquad \qquad \qquad \qquad \qquad \quad }}\LaTeX$✍

❄☃ $\sf(\gray{+}~\red{cores}~\blue{com}~\pink{o}~\orange{App}~\green{Brainly})$ ☘☀

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$\gray{"Absque~sudore~et~labore~nullum~opus~perfectum~est."}$