Calculators

Algebra

Calculator Use

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 is positive a will be positive. If x is negative a will be negative. The Cube Root Calculator 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 \( \sqrt[3]{10} = 2.154435 \).

What is a Cube Root as an Exponent?

The cube root of x is the same as x raised to the 1/3 power. This is written as \( \sqrt[3]{x} = x^{\frac{1}{3}} \).

What is a Cube Root of a Negative Number?

The common definition of the cube root of a negative number is:
(-x)^1/3 = -(x^1/3)

First take the cube root of the number and then make it negative.

Example Cube Roots of Negative Numbers

• 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 Resulting in the Integers 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

Weisstein, Eric W. "Cube Root." From MathWorld -- A Wolfram Web Resource. Cube Root

Math is Fun Cube Roots