Question

a) ⁴√√⁵√7
b) √√80
c) √√162
d) ³√√320​

Answer 1

Resposta:

a) $\sqrt[40]{7}$

b) $2\sqrt[4]{5}$
c) $3\sqrt[4]{2}$
d) $2\sqrt[6]{5}$

Explicação passo a passo:

a) $\sqrt[4]{\sqrt{\sqrt[5]{7}}}=\sqrt[4]{\sqrt[10]{7}}=\left(7^{\frac{1}{10}}\right)^{\frac{1}{4}}=7^{\frac{1}{10}\cdot \frac{1}{4}}=7^{\frac{1}{40}}=\sqrt[40]{7}$

b) $\sqrt{\sqrt{80}}=\sqrt{4\sqrt{5}}=\sqrt{4}\sqrt{\sqrt{5}}=2\sqrt{\sqrt{5}}=2\sqrt[4]{5}$

c) $\sqrt{\sqrt{162}}=\sqrt{\sqrt{2}\cdot \:9}=\sqrt{\sqrt{2}}\sqrt{9}=\sqrt{\sqrt{2}}\cdot \:3=3\sqrt[4]{2}$

d) $\sqrt[3]{\sqrt{320}}=\sqrt[3]{8\sqrt{5}}=\sqrt[3]{8}\sqrt[3]{\sqrt{5}}=2\sqrt[3]{\sqrt{5}}=2\sqrt[6]{5}$