Question

Simplifique: a) $<var>(\sqrt{2})</var>$³ b)$<var>(\sqrt{27})</var>$³ c) $<var>(\sqrt{2})</var>$³ d) $<var>(\sqrt{5})</var>$³ e) $<var>\sqrt\sqrt{48}</var>$ f) ³$<var>\sqrt\sqrt{128}</var>$ g) $<var>\sqrt\sqrt{32}</var>$ h) $<var>\sqrt\sqrt{25}</var>$ i) $<var>\sqrt\sqrt\sqrt{36}</var>$ j) $<var>\sqrt\sqrt{80}</var>$ k) $<var>\sqrt\sqrt{45}</var>$

Answer 1

a) $<var>(\sqrt{2})^{3} = \sqrt{2^{3}} = \sqrt{2^{2}.2} = 2\sqrt{2}</var>$

 

b) $<var>(\sqrt{27})^{3} = \sqrt{27^{3}} = \sqrt{27^{2}.27} = 27\sqrt{27} = 27\sqrt{3^{2}.3} = 27.3\sqrt{3} = 81\sqrt{3}</var>$

 

c) Igual a A

 

d) mesma coisa da A, ficando 5V5

 

e)$<var>\sqrt{\sqrt{48}} = \sqrt{4\sqrt{3}} = \sqrt{2^{2}\sqrt{3}} = 2\sqrt{\sqrt{3}}</var>$

 

f) $<var>\sqrt[3]{\sqrt{128}} = \sqrt[3]{\sqrt{2^{2}.2^{2}.2^{2}.2}} = \sqrt[3]{2.2.2\sqrt{2}} = \sqrt[3]{2^{3}\sqrt{2}} = 2\sqrt[3]{\sqrt{2}}</var>$

 

g)$<var>\sqrt{\sqrt{32}} = \sqrt{4\sqrt{2}} = 2\sqrt{\sqrt{2}}</var>$

 

h) $<var>\sqrt{\sqrt{25}} = \sqrt{5}</var>$

 

i)$<var>\sqrt{\sqrt{\sqrt{36}}} = \sqrt{\sqrt{6}}</var>$

 

j) $<var>\sqrt{\sqrt{80}} = \sqrt{4\sqrt{5}} = 2\sqrt{\sqrt{5}}</var>$

 

k) $<var>\sqrt{\sqrt{45}} = \sqrt{3\sqrt{5}}</var>$