Escreva cada sentença como produto ou quociente de radicais
a)√4×6
b)√7×8
c)√12
4
d)√3²×21
e)³√19³×51²
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Soluções para a tarefa
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24
Basta realizar a fatoração das raízes
![\sqrt{24} = 2 \sqrt{6} \\
\sqrt{56} = 2 \sqrt{14}\\
\sqrt{ \frac{12}{4} } = \sqrt{3} \\
\sqrt{3^2*21} = 3 \sqrt{21}\\
\sqrt[3]{19^3*51^2} = 19 \sqrt[3]{51^2} \\
\sqrt[5]{ \frac{96^7}{32^2} } = \sqrt[5]{ \frac{(2^5*3)^7}{2^{5^2}} } = \sqrt[5]{ \frac{2^{12}*3^7}{2^{10}} } = \sqrt[5]{ 2^2*3^5*3^2 } = 3\sqrt[5]{ 36 }](https://tex.z-dn.net/?f=+%5Csqrt%7B24%7D+%3D+2+%5Csqrt%7B6%7D+%5C%5C%0A+%5Csqrt%7B56%7D++%3D+2+%5Csqrt%7B14%7D%5C%5C%0A+%5Csqrt%7B+%5Cfrac%7B12%7D%7B4%7D+%7D+%3D++%5Csqrt%7B3%7D+++%5C%5C%0A+%5Csqrt%7B3%5E2%2A21%7D+%3D+3+%5Csqrt%7B21%7D%5C%5C%0A+%5Csqrt%5B3%5D%7B19%5E3%2A51%5E2%7D+++%3D++19+%5Csqrt%5B3%5D%7B51%5E2%7D+%5C%5C%0A+%5Csqrt%5B5%5D%7B+%5Cfrac%7B96%5E7%7D%7B32%5E2%7D+%7D+%3D++%5Csqrt%5B5%5D%7B+%5Cfrac%7B%282%5E5%2A3%29%5E7%7D%7B2%5E%7B5%5E2%7D%7D+%7D+%3D++%5Csqrt%5B5%5D%7B+%5Cfrac%7B2%5E%7B12%7D%2A3%5E7%7D%7B2%5E%7B10%7D%7D+%7D++%3D+%5Csqrt%5B5%5D%7B+2%5E2%2A3%5E5%2A3%5E2+%7D+%3D+3%5Csqrt%5B5%5D%7B+36+%7D "\sqrt{24} = 2 \sqrt{6} \\
\sqrt{56} = 2 \sqrt{14}\\
\sqrt{ \frac{12}{4} } = \sqrt{3} \\
\sqrt{3^2*21} = 3 \sqrt{21}\\
\sqrt[3]{19^3*51^2} = 19 \sqrt[3]{51^2} \\
\sqrt[5]{ \frac{96^7}{32^2} } = \sqrt[5]{ \frac{(2^5*3)^7}{2^{5^2}} } = \sqrt[5]{ \frac{2^{12}*3^7}{2^{10}} } = \sqrt[5]{ 2^2*3^5*3^2 } = 3\sqrt[5]{ 36 }")
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