Question

o número
$\sqrt[3]{3 \sqrt{3 } }$
é igual a:

A: 1
B:
$\sqrt{3}$
C:
$\sqrt[6]{9}$
D:
$\sqrt[3]{9}$
E: 3​

Answer 1

Boa tarde!

$\sqrt[3]{3 \sqrt{3 } } = \sqrt[3]{3. {3}^{ \frac{1}{2} } } = \sqrt[3]{3}. \sqrt[3]{ {3}^{ \frac{1}{2} } } = {3}^{ \frac{1}{3} } . ({3}^{ \frac{1}{2} })^{ \frac{1}{3} } = {3}^{ \frac{1}{3} }. {3}^{ \frac{1}{6} } = {3}^{ \frac{1}{3} + \frac{1}{6} } = {3}^{ \frac{2}{6} + \frac{1}{6} } = {3}^{ \frac{3}{6} } = {3}^{ \frac{1}{3} } = \sqrt[3]{3}$