Question

Alguem me ajuda a fazer essa questão ?

Answer 1

Resposta:

$a) \\ \sqrt{12} = \sqrt{2 \times 2 \times 3} = \sqrt{ {2}^{2} \times 3 } = 2 \sqrt{3} \\ \\ b) \\ \sqrt{18} = \sqrt{2 \times 3 \times 3} = \sqrt{ {3}^{2} \times 2} = 3 \sqrt{2} \\ \\ c) \\ \sqrt[3]{24} = \sqrt[3]{2 \times 2 \times 2 \times 3} = \sqrt[3]{ {2}^{3} \times 3} = 2 \sqrt[3]{3} \\ \\ d) \\ \sqrt[4]{32} = \sqrt[4]{2 \times 2 \times 2 \times 2 \times 2} = \sqrt[4]{ {2}^{4} \times 2} = 2 \sqrt[4]{2} \\ \\ e) \\ \sqrt{40} = \sqrt{2 \times 2 \times 2 \times 5} = \sqrt{ {2}^{2} \times 2 \times 5 } = 2 \sqrt{10} \\ \\ f) \\ \sqrt[5]{96} = \sqrt[5]{2 \times 2 \times 2 \times 2 \times 2 \times 3} = \sqrt[5]{ {2}^{5} \times 3} = 2 \sqrt[5]{3} \\ \\ g) \\ \sqrt{ \frac{48}{25} } = \frac{ \sqrt{48} }{ \sqrt{25} } = \frac{ \sqrt{2 \times 2 \times 2 \times 2 \times 3} }{5} = \frac{ \sqrt{ {2}^{2} \times {2}^{2} \times 3 } }{5} = \frac{2 \times 2 \sqrt{3} }{5 } = \frac{4 \sqrt{3} }{5 } \\ \\ h) \\ \sqrt[3]{ \frac{81}{8} } = \frac{ \sqrt[3]{81} }{ \sqrt[3]{8} } = \frac{ \sqrt[3]{3 \times 3 \times 3 \times 3} }{2} = \frac{ \sqrt[3]{ {3}^{3} \times 3} }{2} = \frac{3 \sqrt[3]{3} }{2} \\ \\ i) \sqrt{ \frac{75}{64} } = \frac{ \sqrt{75} }{ \sqrt{64} } = \frac{ \sqrt{5 \times 5 \times 3} }{8} = \frac{ \sqrt{ {5}^{2} \times 3 } }{8} = \frac{5 \sqrt{3} }{8}$