Question

ayudame Sebastián Cortés ​

Answer 1

Respuesta:

1)

$2\sqrt{80} + 9\sqrt{20} - 7\sqrt{45} - 3\sqrt{500}$

$2\sqrt{4^2}\sqrt{5} \\2*4\sqrt{5} \\=8\sqrt{5}$

$9\sqrt{2^2}\sqrt{5} \\9*2\sqrt{5} \\=18\sqrt{5}$

$-7\sqrt{3^2}\sqrt{5} \\ -7*3\sqrt{5} \\= -21\sqrt{5}$

$-3\sqrt{2^2}\sqrt{5^3} \\ -3\sqrt{2^2}\sqrt{5^2}\sqrt{5}\\ -3*2*5\sqrt{5}\\= -30\sqrt{5}$

$8\sqrt{5} + 18\sqrt{5} - 21\sqrt{5} - 30\sqrt{5}\\ = - 25\sqrt{5}$

2)

$\sqrt{175} + \sqrt{243} - \sqrt{63} - 2\sqrt{75}$

$\sqrt{175}\\ \sqrt{5^2}\sqrt{7} \\= 5\sqrt{7}$

$\sqrt{243}\\ \sqrt{3^5}\\ \sqrt{3^4}\sqrt{3}\\ 3^2\sqrt{3}\\ =9\sqrt{3}$

$-\sqrt{63}\\ -\sqrt{3^2}\sqrt{7} \\= -3\sqrt{7}$

$-2\sqrt{75}\\ -2\sqrt{5^2}\sqrt{3} \\ -2*5\sqrt{3}\\ = -10\sqrt{3}$

$5\sqrt{7} - 3\sqrt{7} + 9\sqrt{3} - 10\sqrt{3} \\ = 2\sqrt{7} - \sqrt{3}$

3)

$\sqrt[3]{81} - 3\sqrt[3]{375} + \sqrt[3]{686} + 2\sqrt[3]{648}$

$\sqrt[3]{81} \\ \sqrt[3]{3^4} \\ = 3\sqrt[3]{3}$

$-3\sqrt[3]{375} \\ -3\sqrt[3]{5^3}\sqrt[3]{3} \\ -3*5\sqrt[3]{3} \\ = -15\sqrt[3]{3}$

$\sqrt[3]{686} \\ \sqrt[3]{7^3}\sqrt[3]{2} \\ = 7\sqrt[3]{2}$

$2\sqrt[3]{648} \\ 2\sqrt[3]{2^3}\sqrt[3]{3^4} \\ 2\sqrt[3]{2^3}\sqrt[3]{3^3}\sqrt[3]{3}\\2*2*3\sqrt[3]{3} \\ = 12\sqrt[3]{3}$

$3\sqrt[3]{3} - 15\sqrt[3]{3} + 7\sqrt[3]{2} + 12\sqrt[3]{3} \\ = 4\sqrt[3]{3} + 7\sqrt[3]{2}$