Question

Can someone please explain to me why simplifying the cube root of 500 is 5 cube root 4?

Answer 1

that is a very good question... \[\huge \sqrt[3]{500} \implies \huge \sqrt[3]{5 \times 100} \implies \huge \sqrt[3]{5 \times 5 \times 20} \]
\[\huge \implies \sqrt[3]{5\times 5 \times 5 \times 4} \implies \sqrt[3]{5^3 \times 4}\]
\[\huge \implies \sqrt[3]{5^3} \times \sqrt[3]{4} \implies 5\times \sqrt[3] 4 \implies 5\sqrt[3]4\]
does that help?

Answer 2

Thank you so much!