# Cube Root of a Real Number

## Cube Root of a Real Number

In the equation n$$^{3}$$ = N, the real number n whose cube is equal to N.

### Symbols

The cube root of N is written as $$\sqrt[3]{N}$$ and is read as “the cube root of N“.

### Examples

• If x$$^{3}$$ = 1000, then $$\sqrt[3]{1000}$$ = 10, since 10 × 10 × 10 = 1000.
• If x$$^{3}$$ = –1000, then $$\sqrt[3]{–1000}$$ = –10, since –10 × –10 × –10 = –1000.
• If x$$^{3}$$ = 0.125, then $$\sqrt[3]{0.125}$$ = 0.5, since (0.5) × (0.5) × (0.5)= 0.125.
• If x$$^{3}$$ = $$\frac{1}{8}$$, then $$\sqrt[3]\frac{1}{8}$$ = $$\frac{1}{2}$$, since $$\frac{1}{2}$$ × $$\frac{1}{2}$$ × $$\frac{1}{2}$$ = $$\frac{1}{8}$$