Question

19) escreva no caderno usando um só radical:
a)
$\sqrt{2} \times \sqrt{5}$
b)
$\frac{ \sqrt{5} }{ \sqrt{2} }$
c)
$\sqrt{ \sqrt[3]{5} }$
d)
$\sqrt{2 \sqrt{3} }$
e)
$\sqrt[3]{2} \times \sqrt[4]{2}$
f)
$\sqrt{2} \times \sqrt[3]{2} \times \sqrt[4]{2}$

​

Answer 1

Resposta:

$a)\\ \sqrt{2} \times\sqrt{5} =\sqrt{2\times5} =\sqrt{10 } \\ \\ b)\\ {\sqrt{5} \over\sqrt{2} }=\sqrt{5\div2} \\ \\ c)\\ \sqrt{\sqrt[3]{5} } =\sqrt[2.3]{5} =\sqrt[6]{5} \\ \\ d)\\ \sqrt{2\sqrt{3} } =\sqrt{\sqrt{2^2.3} } =\sqrt[4]{12} \\ \\ e)\\ \sqrt[3]{2} \times\sqrt[4]{2} =\\ \\ reduz~~ao~~mesmo~~\'indice$

Tira mmc divide pelo índice e multiplica pelo expoente do radicando

$\sqrt[12]{2^4}  \times\sqrt[12]{2^3} =\sqrt[12]{2^4.2^3} =\sqrt[12]{2^7 } \\ \\ f)\\ \sqrt{2} \times\sqrt[3]{2} \times\sqrt[4]{2} =\\ \\ mmc~~do~~\'indice~~(2,3,4)=12$

$\sqrt[12]{2^6} \times\sqrt[12]{2^4} \times\sqrt[12]{2^3} =\sqrt[12]{2^6.2^4.2^3} =\sqrt[12]{2^{13}}$