Question

Express as pure surd of order $6:2\times 4^{\frac{1}{3}}$.

Answer 1

$2\sqrt[3]{34}=2(4{)}^{\frac{1}{3}}$
$=\left(8{)}^{\frac{1}{3}}\right(4{)}^{\frac{1}{3}}=(8\times 4{)}^{\frac{1}{3}}$
$=(32{)}^{\frac{1}{3}}={\left(\right(32{)}^{2\times \frac{1}{2}})}^{\frac{1}{3}}$
$={\left(\right(32{)}^2)}^{\frac{1}{2}\times \frac{1}{3}}=(1024{)}^{\frac{1}{6}}$
$=\sqrt[6]{61024}$