Find the cube-roots of 64 x 729

Prime factors of 64:

Prime factors of 729:

$\sqrt[3]{64 \times 729}\\[1em] = \sqrt[3]{64}\times{\sqrt[3]{729}}\\[1em] = \sqrt[3]{(2 \times 2 \times 2)\times(2 \times 2 \times 2)}\times{\sqrt[3]{(3 \times 3 \times 3)\times (3 \times 3 \times 3)}}\\[1em] = (2 \times 2)\times(3 \times 3)\\[1em] = (4)\times(9)\\[1em] = 36$

Hence, $\sqrt[3]{64 \times 729} = 36$