Question

Reduza os radicais na forma mais simples:

$\sqrt{ \frac{64 x^{6} }{9} } =$

Answer 1

Observe que:

$\sqrt{\dfrac{64x^6}{9}}=\dfrac{\sqrt{64x^6}}{\sqrt{9}}$

Por outro lado,

$64x^6=8^2(x^3)^2=(8x^3)^2$

$9=3^2$

Assim, $\dfrac{\sqrt{64x^6}}{\sqrt{9}}=\dfrac{\sqrt{(8x^3)^2}}{\sqrt{3^2}}=\dfrac{8x^3}{3}$

Portanto, $\sqrt{\dfrac{64x^6}{9}}=\dfrac{\sqrt{64x^6}}{\sqrt{9}}=\boxed{\dfrac{8x^3}{3}}$