Question

Resolva as seguintes expressões:

a) 15\⁵√625
b) 18\⁴√81
c) 15\³√5
d) 10\3√5
e) 6\√48

Answer 1

$\frac{15}{ \sqrt[5]{625} }= \frac{15}{ \sqrt[5]{5^4} } * \frac{ \sqrt[5]{5} }{ \sqrt[5]{5} } = \frac{15 \sqrt[5]{5} }{ \sqrt[5]{5^5} } = \frac{15 \sqrt[5]{5} }{5} =3 \sqrt[5]{5}$

$\frac{18}{ \sqrt[4]{81} } = \frac{18}{ \sqrt[4]{3^4} } = \frac{18}{3} = 6$

$\frac{15}{ \sqrt[3]{5} }* \frac{ \sqrt[3]{5^2} }{ \sqrt[3]{5^2} } = \frac{15 \sqrt[3]{5^2} }{ \sqrt[3]{5^3} } = \frac{15 \sqrt[3]{25} }{5} = 3 \sqrt[3]{25}$

$\frac{10}{3 \sqrt{5} } * \frac{ \sqrt{5} }{ \sqrt{5} }= \frac{10 \sqrt{5} }{3.( \sqrt{5)^2} } = \frac{10 \sqrt{5} }{3.5} = \frac{10 \sqrt{5} }{15}= \frac{2 \sqrt{5} }{3}$

$\frac{6}{ \sqrt{48} } = \frac{6}{ \sqrt{2^4.3} }= \frac{6}{4 \sqrt{3} } = \frac{3}{2 \sqrt{3} } * \frac{2 \sqrt{3} }{2 \sqrt{3} }= \frac{6 \sqrt{3} }{4.3} = \frac{6 \sqrt{3} }{12} = \frac{ \sqrt{3} }{2}$