Question

Show that:  \[\sqrt[3]{27} \times \sqrt[3]{64} = \sqrt[3]{27 \times 64}\]

Answer 1

LHS =  \[\sqrt[3]{27} \times \sqrt[3]{64} = \sqrt[3]{3 \times 3 \times 3} \times \sqrt[3]{4 \times 4 \times 4} = 3 \times 4 = 12\]

RHS =  \[\sqrt[3]{27 \times 64} = \sqrt[3]{3 \times 3 \times 3 \times 4 \times 4 \times 4} = \sqrt[3]{\left\{ 3 \times 3 \times 3 \right\} \times \left\{ 4 \times 4 \times 4 \right\}} = 3 \times 4 = 12\]

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