Question

Simplifique as expressões:

a) - √54 - √486 - √294

b) √128 + √50 - √98 + √242

c) cúbica√189 - cúbica√448 - cúbica√875

Answer 1

Resposta:

Fatora os números e aqueles cujo expoente é igual ao índice sai da raiz

$a)\\- \sqrt{54} -\sqrt{486} -\sqrt{294} =\\\\  -\sqrt{2.3^2.3} -\sqrt{2.3^2.3^2.3} -\sqrt{2.3.7^2} =\\ \\ -3\sqrt{2.3} -3.3\sqrt{2.3} -7\sqrt{2.3} =\\ \\ -3\sqrt{6} -9\sqrt{6} -7\sqrt{6} =\\ \\ (-3-9-7)\sqrt{6} =-19\sqrt{6}$

$b)\\ \sqrt{128} +\sqrt{50} -\sqrt{98} +\sqrt{242} =\\ \\ \sqrt{2^6.2} +\sqrt{2.5^2} -\sqrt{2.7^2} +\sqrt{2.11^2} =\\ \\ 2^3\sqrt{2} +5\sqrt{2} -7\sqrt{2} +11\sqrt{2} =\\ \\ (8+5-7+11)\sqrt{2} =\\ \\ (24-7)\sqrt{2} =17\sqrt{2}$

$c)\\ \\ \sqrt[3]{189} -\sqrt[3]{448} -\sqrt[3]{875} =\\ \\ \sqrt[3]{3^3.7} -\sqrt[3]{2^3.2^3.7} -\sqrt[3]{5^3.7} =\\ \\ 3\sqrt[3]{7} -2.2\sqrt[3]{7} -5\sqrt[3]{7} =\\ \\ (3-4-5)\sqrt[3]{7} =\\ \\ (3-9)\sqrt[3]{7} =-6\sqrt[3]{7}$