Question

1.Dê o valor de cada uma das expressões 2. Decomponha o radicando em fatores primos, em seguida use uma das propiedades dos radicais aritmeticos para encontrar o valor da expressao ME AJUDEM

Answer 1

Resposta:

$1)\\ \\ a)~\sqrt[5]{3^{5} } =3^{\frac{5}{5} }=3^{1} =3\\ \\ b)~\sqrt[3]{7^{3} } =7^{\frac{3}{3} } =7^{1} =7\\ \\ c)~\sqrt[7]{(2~.~5)^{7} }=(2~.~5)^{\frac{7}{7} } =(2~.~5)^{1} =2~.~5=10\\ \\ d)~\sqrt{(52^{2})^{2} } =\sqrt{52^{2.2} } =\sqrt{52^{4} }=\sqrt[2]{52^{4} } =52^{\frac{4}{2} } =52^{2} = 2704$

$2)\\ \\ a)~49~|~7\\ ~~~~~~7~|~7\\ ~~~~~~1\\ \\ 7~.~7=7^{2} \\ \\ \sqrt{7^{2} } =7\\ \\ b)~729~|~3\\ ~~~~243~~|~3\\ ~~~~~~81~|~3\\ ~~~~~~27~|~3\\ ~~~~~~~~9~|~3\\ ~~~~~~~~3~|~3\\ ~~~~~~~~1\\ \\ 3.3.3.3.3.3=3^{6} \\ \\ \sqrt[6]{3^{6} }=3^{\frac{6}{6} } =3^{1} =3\\ \\ c)~625~|~5\\ ~~~~125~|~5\\ ~~~~~~25~|~5\\ ~~~~~~~5~|~5\\ ~~~~~~~1\\ \\ 5.5.5.5=5^{2} \\ \\\sqrt[4]{625} =\sqrt[4]{5^{4} } =5^{\frac{4}{4} } =5^{1} =5\\ \\d)\\ \\ \sqrt[10]{1024} \\ \\ 1024~|~2\\ ~~512~|~2\\ ~~256~|~2\\ ~~128~|~2\\ ~~~~64~|~2$

$32~|~2\\ 16~|~2\\ ~~8~|~2\\ ~~4~|~2\\ ~~2~|~2\\ ~~1\\ \\ \sqrt[10]{1024} =\sqrt[10]{2^{10} } =2^{\frac{10}{10} } =2^{1} =2\\ \\ e)~\sqrt[4]{81} \\ \\ 81~|~3\\ 27~|~3\\ ~~9~|~3\\ ~~3~|~3\\ ~~1\\ \\ \sqrt[4]{81} =\sqrt[4]{3^{4} } =3^{\frac{4}{4} }=3^{1} =3\\ \\ f)\\ \\ \sqrt[3]{343} \\ \\ 343~|~7\\ ~~~49~|~7\\ ~~~~7~|~7\\ ~~~~1\\ \\ 7.7.7=7^{3} \\\\ \sqrt[3]{343}=\sqrt[3]{7^{3} } =7^{\frac{3}{3} } =7^{1} =7$