Matemática, perguntado por vitor2005c, 11 meses atrás

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Anexos:

LaizaConfete12: vou responder, um momento

Soluções para a tarefa

Respondido por LaizaConfete12
0

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)

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