\sqrt[3]{80}simplify in simplest radical form

Question

`\sqrt[3]{80}`simplify in simplest radical form

Answer 1

Start by decomposing the number inside the root into primes

Then group the terms into cubes if possible

`\begin{gathered} 80=2\cdot2\cdot2\cdot2\cdot5 \\ 80=2^3\cdot2\cdot5 \\ 80=10\cdot2^3 \end{gathered}`

rewrite the root

`\sqrt[3]{80}=\sqrt[3]{10\cdot2^3}`

then cancel the terms that are cubes and bring them out of the root

`\sqrt[3]{80}=2\sqrt[3]{10}`