Calcule as expressoes abaixo;

a) √242 - √128 -√50=

b)√112+√20-√63+ √125

c)∛378- ∛896+ ∛1750

D) √1.188 - ∛891 + 2 RAIZ 4 DE 2673

Respostas

respondido por: Emerre

Após realizar os cálculos dos devidos exercício concluímos que:

$a)-2\sqrt{2}$

$b)\sqrt{7} +7\sqrt{5}$

$c)3\sqrt[3]{21} -4\sqrt[3]{7} +5\sqrt[3]{14}$

$d)6\sqrt{33} -3\sqrt[3]{33} +6\sqrt[4]{33}$

Para determinar os valores das expressões devemos recorrer a fatoração em números primos.

Uma vez feita a fatoração dos radicandos devemos observar o seu índice e agrupa los de acordo com o seu (índice) expoente

Agrupamos em termos semelhantes, quando possível e efetuamos a sua adição e ou subtração quando possível

a) √242 - √128 -√50=

$a)\sqrt{242} -\sqrt{128} -\sqrt{50} =\\\\\\Fatorando:\\\\\\242/2\\\\121/11\\\\11/11\\\\1\\\\Temos~que~ \sqrt{242} =11\sqrt{2} \\\\\\O ~mesmo~faremos~para~as~ demais\\\\\\128/2\\\\64/2\\\\32/2\\\\16/2\\\\8/2\\\\4/2\\\\2/2\\\\1\\\\Temos~que~\sqrt{128} =8\sqrt{2} \\\\\\50/2\\\\25/5\\\\5/5\\\\1$

$Temos~que~\sqrt{50} =5\sqrt{2} \\\\\\Agora~resolveremos~grupando\\\\\\a)11\sqrt{2} -8\sqrt{2} -5\sqrt{2} =\\\\11\sqrt{2} -13\sqrt{2} =\\\\\\Subrair~dar~sinal~do~maior\\\\\\Resposta\\\\-2\sqrt{2} \\\\\\$

O mesmo faremos para os demais exercícios

$b)\sqrt{112} +\sqrt{20} -\sqrt{63} +\sqrt{125} =\\\\112/2\\\\56/2\\\\28/2\\\\14/2\\\\7/7\\\\1\\\\\sqrt{112} =4\sqrt{7} \\\\\\20/2\\\\10/2\\\\5/5\\\\1\\\\\sqrt{50} =2\sqrt{5} \\\\\\63/3\\\\21/3\\\\7/7\\\\1\\\\\sqrt{63} =3\sqrt{7} \\\\\\125/5\\\\25/5\\\\5/5\\\\1$

$\sqrt{125} =5\sqrt{5}$

Resolvendo:

$b)4\sqrt{7} +2\sqrt{5} -3\sqrt{7} +5\sqrt{5} \\\\\\Agrupando ~em~termos~semelhantes\\\\\\b)4\sqrt{7} -3\sqrt{7} +2\sqrt{5} +5\sqrt{5} \\\\\\Resposta\\\\b)\sqrt{7} +7\sqrt{5}$

$c)\sqrt[3]{378} -\sqrt[3]{896} +\sqrt[3]{1750}=\\ \\\\378/2\\\\189/3\\\\63/3\\\\21/3\\\\7/7\\\\1\\\\\sqrt[3]{378}=3\sqrt[3]{21} \\\\\\896/2\\\\448/2\\\\224/2\\\\112/2\\\\56/2\\\\28/2\\\\14/2\\\\7/7\\\\1\\\\\sqrt[3]{896}=4\sqrt[3]{7} \\\\\\1750/2\\\\875/5/\\\\175/5$

$35/5\\\\7/7\\\\1\\\\\sqrt[3]{896}=5\sqrt[3]{14} \\\\\\Resultado\\\\\\c|)3\sqrt[3]{21} -4\sqrt[3]{7} +5\sqrt[3]{14} \\\\$

$d)\sqrt{1188} -\sqrt[3]{891} +2\sqrt[4]{2673} =\\\\\\1188/2\\\\594/2\\\\297/3\\\\99/3\\\\33/3\\\\11/11\\\\1\\\\\sqrt{1188}=6\sqrt{33} \\\\$

$891/3\\\\297/3\\\\99/3\\\\33/3\\\\11/11\\\\1\\\\\sqrt[3]{891} =3\sqrt[3]{33} \\\\\\2673/3\\\\891/3\\\\297/3\\\\99/3\\\\33/3\\\\11/11\\\\1\\\\2\sqrt[4]{2673} =2\cdot3\sqrt[4]{3\cdot11} \\\\\\2\sqrt[4]{2673}=6\sqrt[4]{33} \\\\\\Resultado\\\\d)6\sqrt{33} -3\sqrt[3]{33} +6\sqrt[4]{33}$