Question

Me ajuda a estudar para a prova e fazer este exercicio

Answer 1

a)

$\sqrt{32 + \sqrt{14 + \sqrt{1 + \sqrt{9} } } } = \\ \sqrt{32 + \sqrt{14 + \sqrt{1 + 3} } } = \\ \sqrt{32 + \sqrt{14 + \sqrt{4} } } = \\ \sqrt{32 + \sqrt{14 + 2} } = \sqrt{32 + \sqrt{16} } = \\ \sqrt{32 + 4} = \sqrt{36} = 6$

b)

$\sqrt{2 + \sqrt{3 + \sqrt{1} } } = \\ \sqrt{2 + \sqrt{3 + 1} } = \sqrt{2 + \sqrt{4} } = \sqrt{2 + 2} = \\ \sqrt{4} = 2$

c)

$\sqrt[3]{1 + \sqrt{49} } = \sqrt[3]{1 + 7} = \sqrt[3]{8} = 2$

d)

$\frac{ \sqrt{16} + \sqrt[6]{64} }{ \sqrt[3]{125} } = \frac{4 + 2}{5} = \frac{6}{5}$

e)

$\sqrt{49} - \sqrt[3]{125} = 7 - 5 = 2$

f)

$\sqrt{10 - \sqrt{1 + 40 \sqrt[3]{8} } } \times \sqrt[10]{1024} = \\ \sqrt{10 - \sqrt{1 + 40 \times 2} } \times 2 = \\ \sqrt{10 - \sqrt{81} } \times 2 = \sqrt{10 - 9} \times 2 = \\ \sqrt{1} \times 2 = 1 \times 2 = 2$