Question

me ajudem pra amanhã por favor​

Answer 1

Resposta:

Explicação passo a passo:

$5. a) 3\sqrt{5} +4\sqrt{3} - \sqrt{5} +8\sqrt{5} \\ 3\sqrt{5} - \sqrt{5} +4\sqrt{3} +8\sqrt{5} \\ 2\sqrt{5} + 12\sqrt{3}$

$b) 7\sqrt[3]{4} - 2\sqrt[3]{4} = 5\sqrt[3]{4}$

$c) 6\sqrt[3]{7} - \sqrt[3]{7} + 2\sqrt{7} + 3\sqrt{7}\\ 5\sqrt[3]{7} + 5\sqrt{7}$

$6. a) 5\sqrt{28} - 3\sqrt{20} -2\sqrt{63} + 2\sqrt{45} \\5\sqrt{2^{2} . 7 } - 3\sqrt{2^{2} . 5 } - 2\sqrt{3^{2} .7 } + 2\sqrt{3^{2} .5 } \\5 .2\sqrt{7} - 3 . 2\sqrt{5} - 2 . 3\sqrt{7} +2 . 3\sqrt{5} \\10\sqrt{7} - 6\sqrt{5} - 6\sqrt{7} +6\sqrt{5} \\10\sqrt{7} - 6\sqrt{7} - 6\sqrt{5} +6\sqrt{5} \\4\sqrt{7}$$b) 8\sqrt{2} -5\sqrt{8} +13\sqrt{18} -15\sqrt{50} -9\sqrt{72} \\8\sqrt{2} -5\sqrt{2^{2}.2 } +13\sqrt{2.3^{2} } -15\sqrt{2.5^{2} } -9\sqrt{2.2^{2}.3^{2}} \\8\sqrt{2} -5.2\sqrt{2} +13.3\sqrt{2} -15.5\sqrt{2} -9.2.3\sqrt{2}\\8\sqrt{2} -10\sqrt{2} +39\sqrt{2} -75\sqrt{2} -54\sqrt{2}\\-2\sqrt{2} +39\sqrt{2} -75\sqrt{2} -54\sqrt{2}\\ +37\sqrt{2} -75\sqrt{2} -54\sqrt{2}\\-38\sqrt{2} -54\sqrt{2}\\ -92\sqrt{2}$

$c) \sqrt[5]{64} - \sqrt[5]{486} - \sqrt[5]{2}\\\sqrt[5]{2^{5}.2 } - \sqrt[5]{3^{5} .2} - \sqrt[5]{2}\\ 2\sqrt[5]{2} - 3\sqrt[5]{2} - \sqrt[5]{2} \\-\sqrt[5]{2} - \sqrt[5]{2} \\-2\sqrt[5]{2}$

$d) 3\sqrt{5} +\sqrt{20} \\ 3\sqrt{5} +\sqrt{2^{2}.5 } \\ 3\sqrt{5} +2\sqrt{5} \\ 5\sqrt{5}$

$7. a) \sqrt{2} .\sqrt{30} = \sqrt{60} = \sqrt{2^{2}.3.5 } =2\sqrt{15}$

$b) \frac{\sqrt{480} }{\sqrt{6} } =\frac{\sqrt{2^{2}.2^{2}.2.3.5 } }{\sqrt{6} } = \frac{4\sqrt{30} }{\sqrt{6} } = \frac{4\sqrt{30} . \sqrt{6} }{\sqrt{6}.\sqrt{6} } = \frac{4\sqrt{180}}{6} = \frac{4\sqrt{2^{2}.3^{2}.5 }}{6} = \frac{4.2.3\sqrt{5} }{6} = \frac{24\sqrt{5} }{6} = 4\sqrt{5}$

$c) \frac{\sqrt{200} }{\sqrt{2} } = \frac{\sqrt{2^{2}.2.5^{2} } }\sqrt{2} } = \frac{2.5\sqrt{5} }{\sqrt{2} } = \frac{10\sqrt{5} }{\sqrt{2} } = \frac{10\sqrt{5}.\sqrt{2} }{\sqrt{2}.\sqrt{2} } = \frac{10\sqrt{10} }{2} = 5\sqrt{10}$

$d) \sqrt{75} . \sqrt{2} = \sqrt{150} = \sqrt{2.3.5^{2} } = 5\sqrt{6}$

$e)\sqrt{180} . \sqrt{3} = \sqrt{2.3.5^{2} } . \sqrt{3} = 5\sqrt{6} . \sqrt{3} = 5\sqrt{18} =5\sqrt{2.3^{2} } = 5.3\sqrt{2} = 15\sqrt{2}$

$f) \frac{\sqrt[3]{720} }{\sqrt[3]{9} } = ) \frac{\sqrt[3]{2^{3}.2.3^{2}.5 } }{\sqrt[3]{9} } = \frac{2\sqrt[3]{90} }{\sqrt[3]{9} } = \frac{2\sqrt[3]{90}.\sqrt[3]{9} }{\sqrt[3]{9}.\sqrt[3]{9} } = \frac{2\sqrt[3]{810} }{9} =\frac{2\sqrt[3]{2.3^{2}.3.5 } }{9} =\frac{2.3\sqrt[3]{30} }{9} =\frac{6\sqrt[3]{30} }{9} = \frac{2\sqrt[3]{30} }{3}$