The cube root of a number is a value that, when multiplied by itself three times, equals the original number. It is denoted as $\sqrt[3]{x}$ or $x^{1/3}$.
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The cube root function is the inverse of the cubic function $f(x) = x^3$.
Cube roots can be both positive and negative. For instance, $\sqrt[3]{-8} = -2$ because $(-2)^3 = -8$.
Unlike square roots, every real number has exactly one real cube root.
The graph of the cube root function $y = \sqrt[3]{x}$ is symmetric with respect to the origin (it exhibits rotational symmetry).
Solving polynomial equations involving cubes often requires finding cube roots.
Review Questions
What is the cube root of $27$?
Explain why $\sqrt[3]{-125} = -5$.
Describe the symmetry property of the graph of the function $y = \sqrt[3]{x}$.
Related terms
Cubic Function: A polynomial function of degree three, typically in the form $f(x) = ax^3 + bx^2 + cx + d$.
Inverse Function: A function that reverses another function. For example, if $f(x) = y$, then its inverse $f^{-1}(y) = x$. The cube root function is an inverse to the cubic function.
$n^{th}$ Root: For any integer $n$, an $n^{th}$ root of a number is a value that, when raised to the power of $n$, equals that number. For example, $\sqrt[n]{x}$ or $x^{1/n}$.