Cube Root of a Real Number
In the equation n[latex]^{3}[/latex] = N, the real number n whose cube is equal to N.
Symbols
The cube root of N is written as [latex]\sqrt[3]{N}[/latex] and is read as "the cube root of N".Examples
- If x[latex]^{3}[/latex] = 1000, then [latex]\sqrt[3]{1000}[/latex] = 10, since 10 × 10 × 10 = 1000.
- If x[latex]^{3}[/latex] = –1000, then [latex]\sqrt[3]{–1000}[/latex] = –10, since –10 × –10 × –10 = –1000.
- If x[latex]^{3}[/latex] = 0.125, then [latex]\sqrt[3]{0.125}[/latex] = 0.5, since (0.5) × (0.5) × (0.5)= 0.125.
- If x[latex]^{3}[/latex] = [latex]\frac{1}{8}[/latex], then [latex]\sqrt[3]\frac{1}{8}[/latex] = [latex]\frac{1}{2}[/latex], since [latex]\frac{1}{2}[/latex] × [latex]\frac{1}{2}[/latex] × [latex]\frac{1}{2}[/latex] = [latex]\frac{1}{8}[/latex]