Question

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Answer 1

respostas

1) a) 2  b) 9

c)

$=\sqrt[3]{1+15}\\=\sqrt[3]{16}\\=\sqrt[3]{2^4}\\=\sqrt[3]{2^3\cdot \:2}\\=\sqrt[3]{2}\sqrt[3]{2^3}\\=2\sqrt[3]{2}$

2) a) $=\sqrt[3]{4^3}$$=4$

b) $=\sqrt[4]{3^4}$ = $3$

c)$=\sqrt[4]{5^4}$ = 5

3)  a)

$10\sqrt{3}+2\sqrt{3}-4\sqrt{3}\\=8\sqrt{3}$

b)

$=3\sqrt{2}-10\sqrt{2}\\=-7\sqrt{2}$

c)

$=3\sqrt{2}+2\sqrt{2}\\=5\sqrt{2}$

4) a)

$=\frac{2\cdot \:2}{2\sqrt{2}}\\=\frac{2}{\sqrt{2}}\\=\frac{\sqrt{2}\sqrt{2}}{\sqrt{2}}\\=\sqrt{2}$

b)

$=\sqrt{\frac{5}{2}}$

c)

$=\frac{1}{\sqrt[5]{216}}\\=\frac{1\cdot \:216^{\frac{4}{5}}}{\sqrt[5]{216}\cdot \:216^{\frac{4}{5}}}\\=\frac{216^{\frac{4}{5}}}{216}\\\\=\frac{2^{\frac{12}{5}}\cdot \:3^{\frac{12}{5}}}{2^3\cdot \:3^3}\\\\=\frac{6^{\frac{2}{5}}}{6}$

d)

$=\frac{2\left(1-\sqrt{2}\right)}{\left(1+\sqrt{2}\right)\left(1-\sqrt{2}\right)}\\\\=\frac{2\left(1-\sqrt{2}\right)}{-1}\\=-2\left(1-\sqrt{2}\right)$

e)

$=\frac{4}{8^{\frac{3}{4}}}\\=\frac{4}{4^{\frac{3}{4}}\cdot \:2^{\frac{3}{4}}}\\\\=\frac{4}{4^{\frac{3}{4}}\cdot \:2^{\frac{3}{4}}}\\\\=\frac{2^{\frac{1}{2}}}{2^{\frac{3}{4}}}\\\\=\frac{1}{2^{\frac{1}{4}}}$