determine o valor real de cada raiz a seguir
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Olá!
a)
![\sqrt[3]{0,216} = \left(\dfrac{216}{1000}\right)^\frac{1}{3} = \left(\dfrac{(2^3\cdot 3^3)^{\frac{1}{3}}}{(10^3)^{\frac{1}{3}}}\right) =
\dfrac{(2^{3\cdot \frac{1}{3}})\cdot (3^{3\cdot \frac{1}{3}})}{10^{3\cdot \frac{1}{3}}} =
\dfrac{2\cdot 3}{10} = \\ \\ \\ = \dfrac{6}{10} = \dfrac{3}{5}.](https://tex.z-dn.net/?f=+%5Csqrt%5B3%5D%7B0%2C216%7D+%3D+%5Cleft%28%5Cdfrac%7B216%7D%7B1000%7D%5Cright%29%5E%5Cfrac%7B1%7D%7B3%7D+%3D+%5Cleft%28%5Cdfrac%7B%282%5E3%5Ccdot+3%5E3%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%7D%7B%2810%5E3%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%7D%5Cright%29+%3D+%0A%5Cdfrac%7B%282%5E%7B3%5Ccdot+%5Cfrac%7B1%7D%7B3%7D%7D%29%5Ccdot+%283%5E%7B3%5Ccdot+%5Cfrac%7B1%7D%7B3%7D%7D%29%7D%7B10%5E%7B3%5Ccdot+%5Cfrac%7B1%7D%7B3%7D%7D%7D+%3D+%0A%5Cdfrac%7B2%5Ccdot+3%7D%7B10%7D+%3D+%5C%5C+%5C%5C+%5C%5C+%3D+%5Cdfrac%7B6%7D%7B10%7D+%3D+%5Cdfrac%7B3%7D%7B5%7D. "\sqrt[3]{0,216} = \left(\dfrac{216}{1000}\right)^\frac{1}{3} = \left(\dfrac{(2^3\cdot 3^3)^{\frac{1}{3}}}{(10^3)^{\frac{1}{3}}}\right) =
\dfrac{(2^{3\cdot \frac{1}{3}})\cdot (3^{3\cdot \frac{1}{3}})}{10^{3\cdot \frac{1}{3}}} =
\dfrac{2\cdot 3}{10} = \\ \\ \\ = \dfrac{6}{10} = \dfrac{3}{5}.")
b)
![\sqrt[3]{\dfrac{14}{125}+\sqrt{\dfrac{3}{5}-\dfrac{11}{25}}}= \sqrt[3]{\dfrac{14}{125}+
\sqrt{\dfrac{4}{25}}} = \sqrt[3]{\dfrac{14}{125}+\dfrac{\sqrt{4}}{\sqrt{25}}} = \\ \\ \\ =
\sqrt[3]{\dfrac{14}{125}+\dfrac{2}{5}} = \sqrt[3]{\dfrac{64}{125}} =
\sqrt[3]{\dfrac{4^3}{5^3}} = \dfrac{\sqrt[3]{4^3}}{\sqrt[3]{5^3}} = \dfrac{4}{5}.](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%5Cdfrac%7B14%7D%7B125%7D%2B%5Csqrt%7B%5Cdfrac%7B3%7D%7B5%7D-%5Cdfrac%7B11%7D%7B25%7D%7D%7D%3D+%5Csqrt%5B3%5D%7B%5Cdfrac%7B14%7D%7B125%7D%2B%0A%5Csqrt%7B%5Cdfrac%7B4%7D%7B25%7D%7D%7D+%3D+%5Csqrt%5B3%5D%7B%5Cdfrac%7B14%7D%7B125%7D%2B%5Cdfrac%7B%5Csqrt%7B4%7D%7D%7B%5Csqrt%7B25%7D%7D%7D+%3D+%5C%5C+%5C%5C+%5C%5C+%3D+%0A%5Csqrt%5B3%5D%7B%5Cdfrac%7B14%7D%7B125%7D%2B%5Cdfrac%7B2%7D%7B5%7D%7D+%3D+%5Csqrt%5B3%5D%7B%5Cdfrac%7B64%7D%7B125%7D%7D+%3D%0A+%5Csqrt%5B3%5D%7B%5Cdfrac%7B4%5E3%7D%7B5%5E3%7D%7D+%3D+%5Cdfrac%7B%5Csqrt%5B3%5D%7B4%5E3%7D%7D%7B%5Csqrt%5B3%5D%7B5%5E3%7D%7D+%3D+%5Cdfrac%7B4%7D%7B5%7D. "\sqrt[3]{\dfrac{14}{125}+\sqrt{\dfrac{3}{5}-\dfrac{11}{25}}}= \sqrt[3]{\dfrac{14}{125}+
\sqrt{\dfrac{4}{25}}} = \sqrt[3]{\dfrac{14}{125}+\dfrac{\sqrt{4}}{\sqrt{25}}} = \\ \\ \\ =
\sqrt[3]{\dfrac{14}{125}+\dfrac{2}{5}} = \sqrt[3]{\dfrac{64}{125}} =
\sqrt[3]{\dfrac{4^3}{5^3}} = \dfrac{\sqrt[3]{4^3}}{\sqrt[3]{5^3}} = \dfrac{4}{5}.")
Bons estudos!
a)
b)
Bons estudos!
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