Question

simplifique as expressões
$\sqrt[3]{189} - \sqrt[3]{448} - \sqrt[3]{875} =$
​URGENTE!!

Answer 1

Explicação passo-a-passo:

$\sqrt[3]{189}-\sqrt[3]{448}-\sqrt[3]{875}$

Fatore todos os números e substitua

    189 = 3³ · 7

    448 = 2⁶ · 7 = 2³ · 2³ · 7

    875 = 5³ · 7

    $\sqrt[3]{189}-\sqrt[3]{448}-\sqrt[3]{875}$ =

    $\sqrt[3]{3^{3}.7}-\sqrt[3]{2^{3}.2^{3}.7}-\sqrt[3]{5^{3}.7}$ =

    $3.\sqrt[3]{7}-2.2.\sqrt[3]{7}-5.\sqrt[3]{7}$ =

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

    $(3-4-5)\sqrt[3]{7}$ = $-6\sqrt[3]{7}$

Resposta:  $-6\sqrt[3]{7}$