Question

(UFRGS). Simplificando $\sqrt{\frac{a}{\sqrt[3]{a} } }$ obtém-se


a) $\sqrt{a}$ b) $\sqrt[3]{a}$ c) $\sqrt[3]{a^{2} }$

Answer 1

Resposta:

b) $\sqrt[3]{a}$

Explicação passo-a-passo:

√$\frac{a}{\sqrt[3]{a} }$

√∛ₐ

$\sqrt[6]{a2}$

$\sqrt[3]{a}$

Answer 2

Explicação passo-a-passo:

Lembre-se que:

• $\sf \sqrt[c]{a^b}=a^{\frac{b}{c}}$

• $\sf \dfrac{a^m}{a^n}=a^{m-n}$

• $\sf \sqrt[c]{\sqrt[b]{a^m}}=\sqrt[c\cdot b]{a^m}$

Assim:

$\sf E=\sqrt{\dfrac{a}{\sqrt[3]{a}}}$

$\sf E=\sqrt{\dfrac{a}{a^{\frac{1}{3}}}}$

$\sf E=\sqrt{a^{1-\frac{1}{3}}}$

$\sf E=\sqrt{a^{\frac{3-1}{3}}}$

$\sf E=\sqrt{a^{\frac{2}{3}}}$

$\sf E=\sqrt{\sqrt[3]{a^2}}$

$\sf E=\sqrt[2\cdot3]{a^2}$

$\sf E=\sqrt[6]{a^2}$

$\sf E=\sqrt[6\div2]{a^{2\div2}}$

$\sf \red{E=\sqrt[3]{a}}$

Letra B