Question

Show that: \[\sqrt[3]{64 \times 729} = \sqrt[3]{64} \times \sqrt[3]{729}\]

Answer 1

LHS =  \[\sqrt[3]{64 \times 729} = \sqrt[3]{4 \times 4 \times 4 \times 9 \times 9 \times 9} = \sqrt[3]{\left\{ 4 \times 4 \times 4 \right\} \times \left\{ 9 \times 9 \times 9 \right\}} = 4 \times 9 = 36\] 

RHS = \[\sqrt[3]{64} \times \sqrt[3]{729} = \sqrt[3]{4 \times 4 \times 4} \times \sqrt[3]{9 \times 9 \times 9} = 4 \times 9 = 36\]

Because LHS is equal to RHS, the equation is true.