simplifique o radical da raiz quinta de 972
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Vamos primeiramente fatorar:
![\begin{array}{c|c}972&2 \\ 486 & 2 \\ 243 & 3 \\ 81 & 3 \\ 27 & 3 \\ 9 & 3 \\ 3 & 3 \\ 1 \end{array} \\\\\\ 972 = 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 = 2^2 \cdot 3^5 \\\\\\\\
\sqrt[5]{942} = ? \\\\ \sqrt[5]{2^2 \cdot 3^5} = ? \\\\ 3 \sqrt[5]{2^2} = ? \\\\ \boxed{3\sqrt[5]{4}}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bc%7Cc%7D972%26amp%3B2+%5C%5C+486+%26amp%3B+2+%5C%5C+243+%26amp%3B+3+%5C%5C+81+%26amp%3B+3+%5C%5C+27+%26amp%3B+3+%5C%5C+9+%26amp%3B+3+%5C%5C+3+%26amp%3B+3+%5C%5C+1+%5Cend%7Barray%7D+%5C%5C%5C%5C%5C%5C+972+%3D+2+%5Ccdot+2+%5Ccdot+3+%5Ccdot+3+%5Ccdot+3+%5Ccdot+3+%5Ccdot+3+%3D+2%5E2+%5Ccdot+3%5E5+%5C%5C%5C%5C%5C%5C%5C%5C%0A%5Csqrt%5B5%5D%7B942%7D+%3D+%3F+%5C%5C%5C%5C+%5Csqrt%5B5%5D%7B2%5E2+%5Ccdot+3%5E5%7D+%3D+%3F+%5C%5C%5C%5C++3+%5Csqrt%5B5%5D%7B2%5E2%7D+%3D+%3F+%5C%5C%5C%5C+%5Cboxed%7B3%5Csqrt%5B5%5D%7B4%7D%7D++ "\begin{array}{c|c}972&2 \\ 486 & 2 \\ 243 & 3 \\ 81 & 3 \\ 27 & 3 \\ 9 & 3 \\ 3 & 3 \\ 1 \end{array} \\\\\\ 972 = 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 = 2^2 \cdot 3^5 \\\\\\\\
\sqrt[5]{942} = ? \\\\ \sqrt[5]{2^2 \cdot 3^5} = ? \\\\ 3 \sqrt[5]{2^2} = ? \\\\ \boxed{3\sqrt[5]{4}}")
DanielSantin:
Reinicia a página se tiver bugado :3
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