Por favor me ajudem na questão abaixo
OBS: Valendo 10 pontos, a resposta certa é a letra b
Anexos:
Leonardo975:
pq c que resposta se u c ja tem a resposta?
eu que a conta
*quero
Soluções para a tarefa
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Olá Geovanna,
boa tarde!
Chegamos na resposta do problema racionalizando (eliminação da raiz) o denominador. Veja:
![\frac{\sqrt[5]{2}+\sqrt[5]{3}+\sqrt[5]{5}}{\sqrt[5]{7^3}}=\\\\\\\frac{\sqrt[5]{2}+\sqrt[5]{3}+\sqrt[5]{5}}{\sqrt[5]{7^3}}\times\frac{\sqrt[5]{7^2}}{\sqrt[5]{7^2}}=\\\\\\\frac{\sqrt[5]{7^2}(\sqrt[5]{2}+\sqrt[5]{3}+\sqrt[5]{5})}{\sqrt[5]{7^3}\cdot\sqrt[5]{7^2}}=\\\\\\\frac{\sqrt[5]{2\cdot7^2}+\sqrt[5]{3\cdot7^2}+\sqrt[5]{5\cdot7^2}}{\sqrt[5]{7^3\cdot7^2}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B5%5D%7B2%7D%2B%5Csqrt%5B5%5D%7B3%7D%2B%5Csqrt%5B5%5D%7B5%7D%7D%7B%5Csqrt%5B5%5D%7B7%5E3%7D%7D%3D%5C%5C%5C%5C%5C%5C%5Cfrac%7B%5Csqrt%5B5%5D%7B2%7D%2B%5Csqrt%5B5%5D%7B3%7D%2B%5Csqrt%5B5%5D%7B5%7D%7D%7B%5Csqrt%5B5%5D%7B7%5E3%7D%7D%5Ctimes%5Cfrac%7B%5Csqrt%5B5%5D%7B7%5E2%7D%7D%7B%5Csqrt%5B5%5D%7B7%5E2%7D%7D%3D%5C%5C%5C%5C%5C%5C%5Cfrac%7B%5Csqrt%5B5%5D%7B7%5E2%7D%28%5Csqrt%5B5%5D%7B2%7D%2B%5Csqrt%5B5%5D%7B3%7D%2B%5Csqrt%5B5%5D%7B5%7D%29%7D%7B%5Csqrt%5B5%5D%7B7%5E3%7D%5Ccdot%5Csqrt%5B5%5D%7B7%5E2%7D%7D%3D%5C%5C%5C%5C%5C%5C%5Cfrac%7B%5Csqrt%5B5%5D%7B2%5Ccdot7%5E2%7D%2B%5Csqrt%5B5%5D%7B3%5Ccdot7%5E2%7D%2B%5Csqrt%5B5%5D%7B5%5Ccdot7%5E2%7D%7D%7B%5Csqrt%5B5%5D%7B7%5E3%5Ccdot7%5E2%7D%7D "\frac{\sqrt[5]{2}+\sqrt[5]{3}+\sqrt[5]{5}}{\sqrt[5]{7^3}}=\\\\\\\frac{\sqrt[5]{2}+\sqrt[5]{3}+\sqrt[5]{5}}{\sqrt[5]{7^3}}\times\frac{\sqrt[5]{7^2}}{\sqrt[5]{7^2}}=\\\\\\\frac{\sqrt[5]{7^2}(\sqrt[5]{2}+\sqrt[5]{3}+\sqrt[5]{5})}{\sqrt[5]{7^3}\cdot\sqrt[5]{7^2}}=\\\\\\\frac{\sqrt[5]{2\cdot7^2}+\sqrt[5]{3\cdot7^2}+\sqrt[5]{5\cdot7^2}}{\sqrt[5]{7^3\cdot7^2}}")
![\frac{\sqrt[5]{2\cdot49}+\sqrt[5]{3\cdot49}+\sqrt[5]{5\cdot49}}{\sqrt[5]{7^5}}=\\\\\\\boxed{\frac{\sqrt[5]{98}+\sqrt[5]{147}+\sqrt[5]{245}}{7}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B5%5D%7B2%5Ccdot49%7D%2B%5Csqrt%5B5%5D%7B3%5Ccdot49%7D%2B%5Csqrt%5B5%5D%7B5%5Ccdot49%7D%7D%7B%5Csqrt%5B5%5D%7B7%5E5%7D%7D%3D%5C%5C%5C%5C%5C%5C%5Cboxed%7B%5Cfrac%7B%5Csqrt%5B5%5D%7B98%7D%2B%5Csqrt%5B5%5D%7B147%7D%2B%5Csqrt%5B5%5D%7B245%7D%7D%7B7%7D%7D "\frac{\sqrt[5]{2\cdot49}+\sqrt[5]{3\cdot49}+\sqrt[5]{5\cdot49}}{\sqrt[5]{7^5}}=\\\\\\\boxed{\frac{\sqrt[5]{98}+\sqrt[5]{147}+\sqrt[5]{245}}{7}}")
boa tarde!
Chegamos na resposta do problema racionalizando (eliminação da raiz) o denominador. Veja:
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