Cube Roots Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Evaluate −1253\sqrt[3]{-125}.

Solution

  1. 1
    A cube root asks for the number whose cube equals the expression inside the radical, so we want x3=−125x^3 = -125.
  2. 2
    Test a likely integer: (−5)3=(−5)(−5)(−5)=25×(−5)=−125(-5)^3 = (-5)(-5)(-5) = 25 \times (-5) = -125.
  3. 3
    Therefore −1253=−5\sqrt[3]{-125} = -5.

Answer

−5-5
Unlike even roots, cube roots of negative numbers are real and negative. If a3=na^3 = n, then n3=a\sqrt[3]{n} = a. This is because a negative times a negative times a negative is negative.

About Cube Roots

The cube root x3\sqrt[3]{x} is the number that, when cubed, gives xx — defined for all real numbers, including negatives.

Learn more about Cube Roots →

More Cube Roots Examples

Example 2 medium

Simplify [formula].

Example 3 medium

Simplify [formula].

Example 4 easy

Evaluate [formula].

Example 5 easy

Evaluate [formula].

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