Question

Alguém me ajuda? Tenho q entregar amanhã

Answer 1

1)

a) $\sqrt[3]{2} .\sqrt[4]{3}=\sqrt[12]{2^4}\sqrt[12]{3^3}=\sqrt[12]{2^4.3^3}=\sqrt[12]{2.6^3}=\sqrt[12]{2.216}=\sqrt[12]{432}$

b) $2\sqrt{3}.5\sqrt[4]{2}=2\sqrt[4]{3^2}.5\sqrt[4]{2}=2\sqrt[4]{3^2.2.5}=2\sqrt[4]{9.2}.5=2\sqrt[4]{18}.5=10\sqrt[4]{18}$

c) $3\sqrt{2}.\sqrt[3]{27}=3\sqrt{2}.3=9\sqrt{2}$

d) $\sqrt[10]{x^3}.\sqrt[5]{x^2}=\sqrt[10]{x^3}\sqrt[10]{x^4}=\sqrt[10]{x^3.x^4}=\sqrt[10]{x^7}$

e) $5.2.\sqrt[3]{3}.\sqrt{5}=5.2\sqrt[6]{3^2}\sqrt[6]{5^3}=5.2\sqrt[6]{3^2.5^3}=5.2\sqrt[6]{9.125}=5.2\sqrt[6]{1125}=10\sqrt[6]{1125}$

f) $\sqrt[4]{3^3}.\sqrt[5]{3^4}.\sqrt[10]{3^7}=\sqrt[20]{3^{15}} \sqrt[20]{3^{16}} \sqrt[20]{3^{14}}=\sqrt[20]{3^{15}.3^{16}.3^{14}}=\sqrt[20]{3^45}}=\sqrt[4]{3^9}=3^2.\sqrt[4]{3}=9\sqrt[4]{3}$

g) $\sqrt[20]{5^{12}}:\sqrt{5}=\sqrt[20]{5^{12}}:\sqrt[20]{5^{10}}=\sqrt[20]{5^2}=\sqrt[10]{5}$

h) $\sqrt[6]{7^2}:\sqrt[10]{7^3}=\sqrt[30]{7^{10}}:\sqrt[30]{7^9}=\sqrt[30]{7}$

2)

a) $\sqrt{3}.(\sqrt{2}-1)=\sqrt{3}\sqrt{2}-\sqrt{3}=\sqrt{6}-\sqrt{3}$

b) $(\sqrt[3]{4}-3).2.\sqrt[3]{2}=2\sqrt[3]{8}-6\sqrt[3]{2}=2.2-6\sqrt[3]{2}=4-6\sqrt[3]{2}$

c) $(2+\sqrt{3}).(2+\sqrt{2})=2.2+2\sqrt{2}+2\sqrt{3}+\sqrt{3}\sqrt{2}=4+2\sqrt{2}+2\sqrt{3}+\sqrt{6}$

d) $(\sqrt{6}+\sqrt{3}).(\sqrt{6}-2\sqrt{3})=6-2\sqrt{18}+\sqrt{18}-6=-6\sqrt{2}+3\sqrt{2}=-3\sqrt{2}$e) $(\sqrt{5}-3\sqrt{2}).(\sqrt{5}+3\sqrt{2})=5-9.2=5-18=-13$

f)