Question

me ajudem por favor ​

Answer 1

Explicação passo-a-passo:

a) $\sqrt[3]{16875}$

   Fatorando o 16875 fica: 15³ . 5

   $\sqrt[3]{15^{3}}.5=15\sqrt{5}$

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b) $\sqrt{288}$

   Fatorando o 288 fica: 12² . 2

   $\sqrt{12^{2}.2}=12\sqrt{2}$

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c) $\sqrt[4]{3888}$

   Fatorando o 3888 fica: 6⁴ . 3

   $\sqrt[4]{6^{4}.3}=6\sqrt[4]{3}$

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d) $\sqrt[3]{135}$

   Fatorando o 135 fica: 3³ . 5

   $\sqrt[3]{3^{3}.5}=3\sqrt[3]{5}$

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e) $\sqrt{420}$

   Fatorando o 420 fica: 2² . 105

   $\sqrt{2^{2}.105}=2\sqrt{105}$

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f) $\sqrt{49a^{4}b^{8}}$

   Fatorando o 49, a⁴ e o $b^{8}$ fica:

        49 = 7²  ;  a⁴ = a² . a²  ;  $b^{8}$ = b² . b² . b² . b²

   $\sqrt{7^{2}.a^{2}.a^{2}.b^{2}.b^{2}.b^{2}.b^{2}}=7.a.a.b.b.b.b=7a^{2}b^{4}$

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g) $\sqrt{9a^{3}b^{5}}$

   Fatorando o 9, a³ e o $b^{5}$ fica

       9 = 3² ; a³ = a² . a ; $b^{5}$ = b² . b² . b

   $\sqrt{3^{2}.a^{2}.a.b^{2}.b^{2}.b}=3.a.b.b\sqrt{a.b}=3ab^{2}\sqrt{ab}$

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h) $\sqrt[3]{27a^{6}b^{12}}$

   Fatorando o 27, $a^{6}$ e o $b^{12}$ fica

       27 = 3³ ; $a^{6}$ = a³ . a³ ; $b^{12}$ = b³ . b³ . b³ . b³

   $\sqrt[3]{3^{3}.a^{3}.a^{3}.b^{3}.b^{3}.b^{3}.b^{3}}=3.a.a.b.b.b.b=3a^{2}b^{4}$

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i) $\sqrt[3]{64a^{5}b^{7}}$

   Fatorando o 64, $a^{5}$ e o $b^{7}$ fica:

       64 = 4³ ; $a^{5}$ = a³ . a² ; $b^{7}$ = b³ . b³ . b

   $\sqrt{4^{3}.a^{3}.a^{2}.b^{3}.b^{3}.b}=4.a.b.b\sqrt{a^{2}.b}=4ab^{2}\sqrt{a^{2}b}$

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j) $\sqrt{16a^{9}b^{4}}$

  Fatorando o 16, $a^{9}$ e o $b^{4}$ fica:

        16 = 2² . 2² ; $a^{9}$ = a² . a² . a² . a² . a ; $b^{4}$ = b² . b²

  $\sqrt{2^{2}.2^{2}.a^{2}.a^{2}.a^{2}.a^{2}.a.b^{2}.b^{2}}=2.2.a.a.a.a.b.b\sqrt{a}=4a^{4}b^{2}\sqrt{a}$