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Cube Root Calculator

Cube Roots Calculator
\[ \sqrt[3]{x} = \; ? \]
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Use this calculator to find the cube root of positive or negative numbers. Given a number x, the cube root of x is a number a such that a3 = x. If x positive a will be positive, if x is negative a will be negative. Cube roots is a specialized form of our common radicals calculator.

Example Cube Roots:

  • The 3rd root of 64, or 64 radical 3, or the cube root of 64 is written as \( \sqrt[3]{64} = 4 \).
  • The 3rd root of -64, or -64 radical 3, or the cube root of -64 is written as \( \sqrt[3]{-64} = -4 \).
  • The cube root of 8 is written as \( \sqrt[3]{8} = 2 \).
  • The cube root of 10 is written as \( \sqrt[3]{10} = 2.154435 \).

The cube root of x is the same as x raised to the 1/3 power. Written as \( \sqrt[3]{x} = x^{\frac{1}{3}} \). The common definition of the cube root of a negative number is that
(-x)1/3
= -(x1/3).[1] For example:

  • The cube root of -27 is written as \( \sqrt[3]{-27} = -3 \).
  • The cube root of -8 is written as \( \sqrt[3]{-8} = -2 \).
  • The cube root of -64 is written as \( \sqrt[3]{-64} = -4 \).

Cube roots (for integer results 1 through 10)

  • Cube root of 1 is 1
  • Cube root of 8 is 2
  • Cube root of 27 is 3
  • Cube root of 64 is 4
  • Cube root of 125 is 5
  • Cube root of 216 is 6
  • Cube root of 343 is 7
  • Cube root of 512 is 8
  • Cube root of 729 is 9
  • Cube root of 1000 is 10

To calculate fractional exponents use our calculator for Fractional Exponents.

References

[1] Weisstein, Eric W. "Square Root." From MathWorld -- A Wolfram Web Resource. Cube Root

Additional reading on cube roots:

Math Forum Is 0 a perfect square?

Math is Fun Cube Roots



 

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Furey, Edward "Cube Root Calculator"; from http://www.calculatorsoup.com - Online Calculator Resource.

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