Simplifique: a) [tex](\sqrt{2})[/tex]³ b)[tex](\sqrt{27})[/tex]³ c) [tex](\sqrt{2})[/tex]³ d) [tex](\sqrt{5})[/tex]³ e) [tex]\sqrt\sqrt{48}[/tex] f) ³[tex]\sqrt\sqrt{128}[/tex] g) [tex]\sqrt\sqrt{32}[/tex] h) [tex]\sqrt\sqrt{25}[/tex] i) [tex]\sqrt\sqrt\sqrt{36}[/tex] j) [tex]\sqrt\sqrt{80}[/tex] k) [tex]\sqrt\sqrt{45}[/tex]
a) [tex](\sqrt{2})^{3} = \sqrt{2^{3}} = \sqrt{2^{2}.2} = 2\sqrt{2}[/tex]
b) [tex](\sqrt{27})^{3} = \sqrt{27^{3}} = \sqrt{27^{2}.27} = 27\sqrt{27} = 27\sqrt{3^{2}.3} = 27.3\sqrt{3} = 81\sqrt{3}[/tex]
c) Igual a A
d) mesma coisa da A, ficando 5V5
e)[tex]\sqrt{\sqrt{48}} = \sqrt{4\sqrt{3}} = \sqrt{2^{2}\sqrt{3}} = 2\sqrt{\sqrt{3}}[/tex]
f) [tex]\sqrt[3]{\sqrt{128}} = \sqrt[3]{\sqrt{2^{2}.2^{2}.2^{2}.2}} = \sqrt[3]{2.2.2\sqrt{2}} = \sqrt[3]{2^{3}\sqrt{2}} = 2\sqrt[3]{\sqrt{2}}[/tex]
g)[tex]\sqrt{\sqrt{32}} = \sqrt{4\sqrt{2}} = 2\sqrt{\sqrt{2}}[/tex]
h) [tex]\sqrt{\sqrt{25}} = \sqrt{5}[/tex]
i)[tex]\sqrt{\sqrt{\sqrt{36}}} = \sqrt{\sqrt{6}}[/tex]
j) [tex]\sqrt{\sqrt{80}} = \sqrt{4\sqrt{5}} = 2\sqrt{\sqrt{5}}[/tex]
k) [tex]\sqrt{\sqrt{45}} = \sqrt{3\sqrt{5}}[/tex]
