Cube Roots & Powers of Roots

What you’ll learn

• Solve $x^3=p$ with one cube root and $x^2=p$ with $\pm$ a square root; scaling every edge by $k$ scales volume by $k^3$.
• Cube root reverses cubing: $\sqrt[3]{V}$ is the edge length of a cube with volume $V$.
• Perfect cubes come from $1^3$ through $5^3$ (and beyond) for quick exact values.
• Estimate $\sqrt[3]{n}$ by trapping $n$ between consecutive cubes, then test nearby decimals by cubing.
• Volume stories for cubes and uniform boxes connect roots to three-dimensional design.
• Keep exact root symbols in formulas; use decimals only when a context calls for rounding.