Question

$\sqrt[5]{48 \times 81}$

Answer 1

$\sqrt[5]{48 \times 81} = \sqrt[5]{16 \times 3 \times 9 \times 9} = \sqrt[5]{ \frac{32}{2} \times {3}^{5} } = \\ = \sqrt[5]{ \frac{ {2}^{5} \times {3}^{5} }{2} } = \frac{ \sqrt[5]{ {(2 \times 3)}^{5} } }{ \sqrt[5]{2} } = \frac{6}{ \sqrt[5]{2} } = \\ = \frac{6 \sqrt[5]{16} }{ \sqrt[5]{2} \times \sqrt[5]{16} } = \frac{6 \sqrt[5]{16} }{ \sqrt[5]{32} } = \frac{6 \sqrt[5]{16} }{2} = 3 \sqrt[5]{16}$