Question

simplifique
A)
${ \sqrt{7} }^{2} =$


B)
${5} \sqrt{13} ^{5} =$


C)
$\sqrt[5]{32} =$


D)
$\sqrt{4 \sqrt{3 \sqrt{2} } } =$


E)
$\sqrt{3 \sqrt{4 \sqrt{5 \sqrt{7} } } }$



F)
$\sqrt{4 \sqrt{3 \sqrt{52} } }$
​

Answer 1

Resposta passo a passo:

A)

$\sqrt{7} ^{2} \\\\\sqrt{7^{2} } \\\\7^{\frac{2}{2} } \\\\7^{1} \\\\7$

B)

$5\sqrt{13} ^{5} \\\\5\sqrt{13^{5} } \\\\5\sqrt{13^{4}\times13 } \\\\5\sqrt{13^{4} } \times\sqrt{13} \\\\5\times13^{\frac{4}{2} } \times\sqrt{13} \\\\5\times13^{2} \sqrt{13} \\\\5\times169\sqrt{13} \\\\845\sqrt{13}$

C)

$\sqrt[5]{32} \\\\\sqrt[5]{2^{5} } \\\\2^{\frac{5}{5} } \\\\2^{1} \\\\2$

D)

$\sqrt{4\sqrt{3\sqrt{2} } } \\\\\sqrt{4} \times\sqrt{\sqrt{3\sqrt{2}} } \\\\\sqrt{2^{2} } \times\sqrt{\sqrt{3} }\times\sqrt{\sqrt{\sqrt{2} } } \\\\2^{\frac{2}{2} } \times\sqrt[2^{2} ]{3} \times\sqrt[2^{3} ]{2} \\\\2^{1} \times\sqrt[4]{3} \times\sqrt[8]{2} \\\\2\sqrt[4]{3} \sqrt[8]{2}$

E)

$\sqrt{3\sqrt{4\sqrt{5\sqrt{7} } } } \\\\\sqrt{3\times\sqrt{4 } \times\sqrt{\sqrt{5\sqrt{7} }} }\\\\\sqrt{3\times\sqrt{2^{2} } \times\sqrt{\sqrt{5\sqrt{7} }} }\\\\\sqrt{3\times2 \times\sqrt{\sqrt{5\sqrt{7} }} }\\\\\sqrt{6 \times\sqrt{\sqrt{5\sqrt{7} }} }\\\\\sqrt{6 \times\sqrt[2^{2} ]{5\sqrt{7}} }\\\\\sqrt{6 \times\sqrt[4 ]{5\sqrt{7}} }\\\\\sqrt{6} \times \sqrt{\sqrt[4]{5\sqrt{7} } } \\\\\sqrt{6} \times \sqrt[2\times4]{5\sqrt{7}}\\\\\sqrt{6} \times \sqrt[8]{5\sqrt{7}}$

$\sqrt{6} \times \sqrt[8]{5}\times\sqrt[8]{\sqrt{7}} \\\\\sqrt{6} \times \sqrt[8]{5}\times\sqrt[8\times2]{7}\\\\\sqrt{6} \times \sqrt[8]{5}\times\sqrt[16]{7}\\\\\sqrt{6} \sqrt[8]{5}\sqrt[16]{7}$

F)

$\sqrt{4\sqrt{3\sqrt{52} } } \\\\\sqrt{4} \times\sqrt{\sqrt{3\sqrt{4\times13} } } \\\\\sqrt{2^{2} } \times\sqrt{\sqrt{3\sqrt{4}\times\sqrt{13} } }\\\\2^{\frac{2}{2} } \times\sqrt{\sqrt{3\sqrt{2^{2} }\times\sqrt{13} } }\\\\2^{1} \times\sqrt{\sqrt{3\times2^{\frac{2}{2} } \times\sqrt{13} } }\\\\2 \times\sqrt{\sqrt{3\times2^{1} \times\sqrt{13} } }\\\\2 \times\sqrt{\sqrt{3\times2 \times\sqrt{13} } }\\\\2 \times\sqrt{\sqrt{6 \times\sqrt{13} } }$

$2 \times\sqrt{\sqrt{6} } \times\sqrt{\sqrt{\sqrt{13} } } \\\\2 \times\sqrt[2^{2} ]{6} \times\sqrt[2^{3} ]{13} \\\\2 \times\sqrt[4]{6} \times\sqrt[8]{13}\\\\2\sqrt[4]{6}\sqrt[8]{13}$