This online cube root calculator finds all cube roots of positive or negative real numbers. There are one real (the principal) and two complex conjugate cube roots for any nonzero real number.
x = a1/3
How to find cube root
The cube root of \(a\) (denoted \(\sqrt[3]{a}\) or \(a^{\frac13}\) ) is a number \(x\) such that \({ x }^{ 3 } = a\). If \(a\) is positive \(x\) will be positive, if \(a\) is negative \(x\) will be negative. In general \(\sqrt[3]{-a} = -\sqrt[3]{a}\).
The equation \({ x }^{ 3 } = a\) is a special form of cubic equation. If \({ x }_{ 1 }\) is the real root of this equation, then the two complex roots can be found from the following formulas:
$${ x }_{ 2 }=\left(-\frac{1}{2}+\frac{\sqrt{3}}{2}i\right){ x }_{ 1 }, \quad { x }_{ 3 }=\left(-\frac{1}{2}-\frac{\sqrt{3}}{2}i\right){ x }_{ 1 }.$$
Principal cube roots for integer results 1 through 10 are as follows:
• 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
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