Decomponha o radicando em fatores primos e simplifique os radicais.
a) raiz quarta de 0,36
b) raiz sexta de 0,216
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a) ![\sqrt[4]{0,36} = \sqrt[4]{ \frac{36}{100} } = \sqrt[4]{ \frac{ 6^{2} }{ 10^{2} } } = \sqrt{\frac{ 6 }{ 10 }} = \sqrt{\frac{ 3 }{ 5 }} = \frac{ \sqrt{3} }{ \sqrt{5} } =\frac{ \sqrt{3} . \sqrt{5} }{ \sqrt{5} . \sqrt{5}} = \frac{\sqrt{15}}{5}](https://tex.z-dn.net/?f=+%5Csqrt%5B4%5D%7B0%2C36%7D+%3D+%5Csqrt%5B4%5D%7B+%5Cfrac%7B36%7D%7B100%7D+%7D+%3D+%5Csqrt%5B4%5D%7B+%5Cfrac%7B+6%5E%7B2%7D+%7D%7B+10%5E%7B2%7D+%7D+%7D+%3D+%5Csqrt%7B%5Cfrac%7B+6+%7D%7B+10+%7D%7D+%3D+%5Csqrt%7B%5Cfrac%7B+3+%7D%7B+5+%7D%7D+%3D+%5Cfrac%7B+%5Csqrt%7B3%7D+%7D%7B+%5Csqrt%7B5%7D+%7D+%3D%5Cfrac%7B+%5Csqrt%7B3%7D+.+%5Csqrt%7B5%7D+%7D%7B+%5Csqrt%7B5%7D+.+%5Csqrt%7B5%7D%7D+%3D+%5Cfrac%7B%5Csqrt%7B15%7D%7D%7B5%7D+ "\sqrt[4]{0,36} = \sqrt[4]{ \frac{36}{100} } = \sqrt[4]{ \frac{ 6^{2} }{ 10^{2} } } = \sqrt{\frac{ 6 }{ 10 }} = \sqrt{\frac{ 3 }{ 5 }} = \frac{ \sqrt{3} }{ \sqrt{5} } =\frac{ \sqrt{3} . \sqrt{5} }{ \sqrt{5} . \sqrt{5}} = \frac{\sqrt{15}}{5}")
b)![\sqrt[6]{0,216} = \sqrt[6]{ \frac{216}{1000} } = \sqrt[6]{ \frac{ 2^{3}. 3^{3} }{ 10^{3} } } = \sqrt{\frac{ 2.3 }{ 10 }} = \sqrt{\frac{ 3 }{ 5 }} = \frac{ \sqrt{3} }{ \sqrt{5} } =\frac{ \sqrt{3} . \sqrt{5} }{ \sqrt{5} . \sqrt{5}} = \frac{\sqrt{15}}{5}](https://tex.z-dn.net/?f=%5Csqrt%5B6%5D%7B0%2C216%7D+%3D+%5Csqrt%5B6%5D%7B+%5Cfrac%7B216%7D%7B1000%7D+%7D+%3D+%5Csqrt%5B6%5D%7B+%5Cfrac%7B+2%5E%7B3%7D.+3%5E%7B3%7D++%7D%7B+10%5E%7B3%7D+%7D+%7D+%3D+%5Csqrt%7B%5Cfrac%7B+2.3+%7D%7B+10+%7D%7D+%3D+%5Csqrt%7B%5Cfrac%7B+3+%7D%7B+5+%7D%7D+%3D+%5Cfrac%7B+%5Csqrt%7B3%7D+%7D%7B+%5Csqrt%7B5%7D+%7D+%3D%5Cfrac%7B+%5Csqrt%7B3%7D+.+%5Csqrt%7B5%7D+%7D%7B+%5Csqrt%7B5%7D+.+%5Csqrt%7B5%7D%7D+%3D+%5Cfrac%7B%5Csqrt%7B15%7D%7D%7B5%7D+ "\sqrt[6]{0,216} = \sqrt[6]{ \frac{216}{1000} } = \sqrt[6]{ \frac{ 2^{3}. 3^{3} }{ 10^{3} } } = \sqrt{\frac{ 2.3 }{ 10 }} = \sqrt{\frac{ 3 }{ 5 }} = \frac{ \sqrt{3} }{ \sqrt{5} } =\frac{ \sqrt{3} . \sqrt{5} }{ \sqrt{5} . \sqrt{5}} = \frac{\sqrt{15}}{5}")
b)
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