Question

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Answer 1

Olá!

Vamos lá:

a) $\sqrt{2}$ · $\sqrt{18}$ =

$\sqrt{(2 . 18)}$ = $\sqrt{36}$

b) $\frac{\sqrt{6}}{5}$ · $\frac{\sqrt{12}}{3}$ =

$\frac{\sqrt{(6 . 12)}}{(5 . 3)}$ = $\frac{\sqrt{72}}{15}$

c) $\frac{\sqrt[5]{b^{3}}}{\sqrt{3}}$ · $\frac{\sqrt[5]{b^{2}}}{\sqrt{3}}$ =

$\frac{\sqrt[5]{(b^{3} . b^{2})}}{\sqrt{(3 . 3)}}$ =

$\frac{\sqrt[5]{b^{(3 + 2)}}}{\sqrt{9}}$ =

$\frac{\sqrt[5]{b^{5}}}{3}$ = $\frac{b}{3}$

d) $\sqrt[3]{8^{4}}$ · $\sqrt[4]{8^{3}}$ =

MMC(3,4) = 12

$\sqrt[12]{8^{[4 . (12 : 3)]}}$ · $\sqrt[12]{8^{[3 . (12 : 4)]}}$ =

$\sqrt[12]{8^{16}}$ · $\sqrt[12]{8^{9}}$ =

$\sqrt[12]{8^{16} . 8^{9}}$ =

$\sqrt[12]{8^{(16 + 9)}}$ = $\sqrt[12]{8^{25}}$

e) $\sqrt{\sqrt[3]{4}}$ ÷ $\sqrt[5]{\sqrt{2}}$ =

$\sqrt[(2 . 3)]{4}$ ÷ $\sqrt[(5 . 2)]{2}$ =

$\sqrt[6]{4}$ ÷ $\sqrt[10]{2}$ =

MMC(6, 10) = 30

$\sqrt[30]{4^{5}}$ ÷ $\sqrt[30]{2^{3}}$ =

$\sqrt[30]{(2^{2})^{5}}$ ÷ $\sqrt[30]{2^{3}}$ =

$\sqrt[30]{2^{(2 . 5)}}$ ÷ $\sqrt[30]{2^{3}}$ =

$\sqrt[30]{2^{10}}$ ÷ $\sqrt[30]{2^{3}}$ =

$\sqrt[30]{(2^{10} : 2^{3})}$ =

$\sqrt[30]{2^{(10 - 3)}}$ = $\sqrt[30]{2^{7}}$

f) $\sqrt{\sqrt{\sqrt{7^{3}}}}$ ÷ $\sqrt[4]{\sqrt{7}}$ =

$\sqrt[4]{\sqrt{7^{3}}}$ ÷ $\sqrt[4]{\sqrt{7}}$ =

$\sqrt[4]{(\sqrt{7^{3} : \sqrt{7}})}$ =

$\sqrt[4]{\sqrt{(7^{3} : 7)}}$ =

$\sqrt[4]{\sqrt{7^{(3 - 1)}}}$ =

$\sqrt[4]{\sqrt{7^{2}}}$ = $\sqrt[4]{7}$

Abraços!