Question

$\sqrt[3]{2} * \sqrt{5}$

Answer 1

Express the radicals in fractional exponent form and combine using the exponent rules :

$\sqrt[3]{2}*\sqrt{5}$

$=2^{\frac{1}{3}}*5^{\frac{1}{2}}$

$=2^{\frac{2}{6}}*5^{\frac{3}{6}}$

$=4^{\frac{1}{6}}*125^{\frac{1}{6}}$

$=(4*125)^{\frac{1}{6}}$

$=(500)^{\frac{1}{6}}$

$=\sqrt[6]{500}$