Question

calcule as adições e subtração abaixo e dê o resultado na forma simplificada .

​

Answer 1

I. Fatorando:

8 = 2 . 2 . 2 → 8 = 2³

18 = 2 . 3 . 3 → 18 = 2 . 3²

32 = 2 . 2 . 2 . 2 . 2 → 32 = $2^{5}$

72 = 2 . 2 . 2 . 3 . 3 → 72 = 2³ . 3²

Calculando:

$5\sqrt{8} +7\sqrt{18} +\sqrt{32} -3\sqrt{72} =\\\\5\sqrt{2^{3} }+7\sqrt{2\:.\:3^{2} } +\sqrt{2^{5} } -3\sqrt{2^{3}\:.\:3^{2} } =\\\\5\:.\:2\sqrt{2} +7\:.\:3\sqrt{2} +2^{2} \sqrt{2} -3\:.\:2\:.\:3\sqrt{2} =\\\\10\sqrt{2} +21\sqrt{2} +4\sqrt{2} -18\sqrt{2} =\\\\31\sqrt{2} +4\sqrt{2} -18\sqrt{2}=\\\\35\sqrt{2} -18\sqrt{2} =\\\\17\sqrt{2}$

II. Fatorando:

12 = 2 . 2 . 3 → 12 = 2² . 3

27 = 3 . 3 . 3 → 27 = 3³

75 = 3 . 5 . 5 → 75 = 3 . 5²

48 = 2 . 2 . 2 . 2 . 3 → 48 = $2^{4}$ . 3

Calculando:

$8\sqrt{12} -5\sqrt{27} +\sqrt{75} +2\sqrt{48} =\\\\8\sqrt{2^{2} \:.\:3} -5\sqrt{3^{3} } +\sqrt{3\:.\:5^{2} } +2\sqrt{2^{4}\:.\:3 } =\\\\8\:.\:2\sqrt{3} -5\:.\:3\sqrt{3} +5\sqrt{3} +2\:.\:2\:.\:2\sqrt{3} =\\\\16\sqrt{3} -15\sqrt{3} +5\sqrt{3} +8\sqrt{3} =\\\\\sqrt{3} +5\sqrt{3} +8\sqrt{3} \\\\6\sqrt{3} +8\sqrt{3} =\\\\14\sqrt{3}$

Espero ter ajudado!

Desculpe qualquer erro.