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Cube root

from class:

Algebra and Trigonometry

Definition

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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5 Must Know Facts For Your Next Test

  1. The cube root function is the inverse of the cubic function $f(x) = x^3$.
  2. Cube roots can be both positive and negative. For instance, $\sqrt[3]{-8} = -2$ because $(-2)^3 = -8$.
  3. Unlike square roots, every real number has exactly one real cube root.
  4. The graph of the cube root function $y = \sqrt[3]{x}$ is symmetric with respect to the origin (it exhibits rotational symmetry).
  5. 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 $y = \sqrt[3]{x}$.
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