Question

ajuda aí ????????.....

Answer 1

Exercício 5:

a)

$2\sqrt{75}+2\sqrt{3}-2\sqrt{12}\\\\2\sqrt{3.5^{2}}+2\sqrt{3}-2\sqrt{2^{2}.3}\\\\2.5\sqrt{3}+2\sqrt{3}-2.2\sqrt{3}\\\\10\sqrt{3}+2\sqrt{3}-4\sqrt{3}\\\\8\sqrt{3}$

b)

$\sqrt{50}+\sqrt{18}-\sqrt{8}\\\\\sqrt{2.5^{2} }+\sqrt{2.3^{2} }-\sqrt{2^{3}}\\\\5\sqrt{2}+3\sqrt{2}-2\sqrt{2}\\\\6\sqrt{2}$

Exercício 6:

$\sqrt{75}:\sqrt{3}=\sqrt{75:3}=\sqrt{25}=5$

$\sqrt{2}.\sqrt{10}=\sqrt{2.10} =\sqrt{20}=\sqrt{2^{2}.5}=2\sqrt{5}$

$\sqrt[3]{32}:\sqrt[3]{16}=\sqrt[3]{32:16}=\sqrt[3]{2}$

$\sqrt[3]{3}.\sqrt[3]{9}=\sqrt[3]{3.9}=\sqrt[3]{27}=3$

Exercício 7:

a) $\sqrt{\sqrt[3]{\sqrt{2}}}=\sqrt[2.3.2]{2}=\sqrt[12]{2}$

b) $\sqrt[4]{\sqrt{7}}=\sqrt[4.2]{7}=\sqrt[8]{7}$

Exercício 8:

$\sqrt[3]{12^{3}}=12$

$\sqrt[5]{121^{5}}=121$

$\sqrt[7]{17^{7}}=17$

Exercício 9:

$x\sqrt[3]{x}=\sqrt[3]{x.x^{3}}=\sqrt[3]{x^{4} }$

$3\sqrt{5}=\sqrt{5.3^{2}}=\sqrt{5.9}=\sqrt{45}$

$2a\sqrt{a}=\sqrt{a.2^{2}.a^{2}}=\sqrt{4a^{3}}$

Exercício 10:

c) $\sqrt[9]{512}=\sqrt[9]{2^{9}}=2$

d) $\sqrt[4]{176}=\sqrt[4]{2^{4}.11 }=2\sqrt[4]{11}$