Cube Roots Math Example 3

Solution

1. 1
   Factor the radicand: $216 = 6^3$ and $x^6 = (x^2)^3$, so $216x^6 = 6^3 \cdot (x^2)^3$.
2. 2
   Apply the cube root to each factor: $\sqrt[3]{6^3 \cdot (x^2)^3} = \sqrt[3]{6^3} \cdot \sqrt[3]{(x^2)^3}$.
3. 3
   Simplify: $\sqrt[3]{6^3} = 6$ and $\sqrt[3]{(x^2)^3} = x^2$. Therefore $\sqrt[3]{216x^6} = 6x^2$.