Question

$5 \sqrt[12]{64} - \sqrt{18} \: sobre \: \sqrt{50} - \sqrt[4]{324} \:$
é igual a ?​

Answer 1

Resposta:

Explicação passo-a-passo:

vamos por partes

$\sqrt[12]{64}=\sqrt[12]{2^{6}}\\\\Simplificando\\\\\sqrt[12]{64}=\sqrt{2}$

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$\sqrt{18}=\sqrt{9.2}\\\\\sqrt{18}=\sqrt{9}.\sqrt{2}\\\\\sqrt{18}=3\sqrt{2}$

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$\sqrt{50}=\sqrt{25.2}\\\\\sqrt{50}=\sqrt{25}.\sqrt{2}\\\\\sqrt{50}=5\sqrt{2}$

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$\sqrt[4]{324}=\sqrt[4]{3^{4}.2^{2}}\\\\\sqrt[4]{324}=\sqrt[4]{3^{4}}.\sqrt[4]{2^{2}}\\\\\sqrt[4]{324}=3\sqrt{2}$

Substituindo na expressão inicial

$\dfrac{5\sqrt[12]{64}-\sqrt{18}}{\sqrt{50}-\sqrt[4]{324}}=\dfrac{5\sqrt{2}-3\sqrt{2}}{5\sqrt{2}-3\sqrt{2}}=1$