Cube root

Definition

A cube root of a number is a value that, when multiplied by itself three times (cubed), gives the original number. Mathematically, if $x^3 = a$, then $x$ is the cube root of $a$, denoted as $\sqrt[3]{a}$.

5 Must Know Facts For Your Next Test

1. The cube root function is the inverse of the cubic function.
2. Every real number has exactly one real cube root.
3. The graph of the cube root function $f(x) = \sqrt[3]{x}$ has an inflection point at the origin (0,0).
4. Cube roots can be both positive and negative because cubing a negative number yields a negative result.
5. The domain and range of the cube root function are all real numbers.

Review Questions

• What is the cube root of -27?
• If $x^3 = 64$, what is $x$?
• Explain why every real number has exactly one real cube root.

Related terms

Cubic Function:

A polynomial function in which the highest-degree term is cubed, typically expressed as $f(x) = ax^3 + bx^2 + cx + d$.

Inverse Function:

A function that reverses another function; if $f(x)$ maps x to y, then its inverse $f^{-1}(y)$ maps y back to x.

Radical Expression: An expression that contains a square root, cube root, or higher roots symbol.